ORIGINAL_ARTICLE
Zagreb Indices and Coindices of Total Graph, Semi-Total Point Graph and Semi-Total Line Graph of Subdivision Graphs
Expressions for the Zagreb indices and coindices of the total graph, semi-total point graph and of semi-total line graph of subdivision graphs in terms of the parameters of the parent graph are obtained, thus generalizing earlier existing results.
https://mir.kashanu.ac.ir/article_95588_beb81a85be57455f29b1a0a7dec61bd4.pdf
2020-03-01
1
12
10.22052/mir.2018.134814.1103
Zagreb indices
Zagreb coindices
total graph
semi-total point graph
semi-total line graph
subdivision graph
Harishchandra S.
Ramane
hsramane@yahoo.com
1
Department of Mathematics, Karnatak University, Dharwad, India
AUTHOR
Saroja Y.
Talwar
saroyatalwar@gmail.com
2
Department of Mathematics, Karnatak University, Dharwad, India
AUTHOR
Ivan
Gutman
gutman@kg.ac.rs
3
Faculty of Science, University of Kragujevac, Kragujevac, Serbia
LEAD_AUTHOR
[1] A. R. Ashrafi, T. Došlic and A. Hamzeh, The Zagreb coindices of graph operations, Discrete Appl. Math. 158 (2010) 1571–1578.
1
[2] B. Borovicanin, K. C. Das, B. Furtula and I. Gutman, Bounds for Zagreb indices, MATCH Commun. Math. Comput. Chem. 78 (2017) 17–100.
2
[3] J. Devillers and A. T. Balaban, Topological Indices and Related Descriptors in QSAR and QSPR, Gordon & Breach Science, Amsterdam, 1999.
3
[4] T. Došlic, Vertex–weighted Wiener polynomials for composite graphs, Ars Math. Comtemp. 1 (2008) 66–80.
4
[5] I. Gutman, Degree–based topological indices, Croat. Chem. Acta 86 (2013) 351–361.
5
[6] I. Gutman, B. Furtula, Ž. Kovijanic Vukicevic and G. Popivoda, On Zagreb indices and coindices, MATCH Commun. Math. Comput. Chem. 74 (2015) 5–16.
6
[7] F. Harary, Graph Theory, Addison Wesley, Reading, 1969.
7
[8] G. Mohanappriya and D. Vijayalakshmi, Topological indices of total graph of subdivision graphs, Ann. Pure Appl. Math. 14 (2017) 231–235.
8
[9] H. S. Ramane, V. V. Manjalapur and I. Gutman, General sum-connectivity index, general product-connectivity index, general Zagreb index and coindices of line graph of subdivision graphs, AKCE Int. J. Graphs Comb. 14 (2017) 92–100.
9
[10] P. S. Ranjini, V. Lokesha and I. N. Cangül, On the Zagreb indices of the line graphs of the subdivision graphs, Appl. Math. Comput. 218 (2011) 699–702.
10
[11] E. Sampathkumar and S. B. Chikkodimath, Semi-total graphs of a graph, I, II, III, J. Karnatak Univ. Sci. 18 (1973) 274–280.
11
[12] R. Todeschini and V. Consonni, Molecular Descriptors for Chemoinformatics, Wiley–VCH Verlag GmbH & Co. KGaA, Weinheim, 2009.
12
ORIGINAL_ARTICLE
Some Graph Polynomials of the Power Graph and its Supergraphs
In this paper, exact formulas for the dependence, independence, vertex cover and clique polynomials of the power graph and its supergraphs for certain finite groups are presented.
https://mir.kashanu.ac.ir/article_96959_b6e64d2437a2e69156ba43083ceabd35.pdf
2020-03-01
13
22
10.22052/mir.2019.173747.1121
Dependence polynomial
independence polynomial
vertex cover polynomial
clique polynomial
power graph
Asma
Hamzeh
hamze2006@yahoo.com
1
Property and Casualty (Non-life) Insurance Research Group, Insurance Research Center, Tehran, Iran
LEAD_AUTHOR
[1] T. Došlic, Splices, links, and their degree-weighted Wiener polynomials, Graph
1
Theory Notes N. Y. 48 (2005) 47 - 55.
2
[2] M. Feng, X. Ma and K. Wang, The structure and metric dimension of the
3
power graph of a finite group, European J. Combin. 43 (2015) 82 - 97.
4
[3] D. C. Fisher and A. E. Solow, Dependence polynomial, Discrete Math. 82
5
(1990) 251 - 258.
6
[4] A. Hamzeh and A. R. Ashrafi, The order supergraph of the power graph of a
7
finite group, Turkish J. Math. 42 (2018) 1978 - 1989.
8
[5] A. Hamzeh and A. R. Ashrafi, Automorphism group of supergraphs of the
9
power graph of a finite group, European J. Combin. 60 (2017) 82 - 88.
10
[6] A. Hamzeh and A. R. Ashrafi, Spectrum and L-spectrum of the power graph
11
and its main supergraph for certain finite groups, Filomat 31(16) (2017)
12
5323 - 5334.
13
[7] A. V. Kelarev and S. J. Quinn, A combinatorial property and power graphs of
14
groups, Contributions to general algebra 12 (Vienna, 1999), 229-235, Heyn,
15
Klagenfurt, 2000.
16
[8] X. L. Ma, H. Q. Wei and G. Zhong, The cyclic graph of a finite group, Algebra
17
2013 (2013) 7 pp.
18
[9] Z. Mehranian, A. Gholami and A. R. Ashrafi, A note on the power graph of
19
a finite group, Int. J. Group Theory 5(1) (2016) 1 - 10.
20
[10] J. S. Rose, A Course on Group Theory, Cambridge University Prees, Cambridge,
21
New York- Melbourne, 1978.
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[11] G. Sabidussi, Graph derivatives, Math. Z. 76 (1961) 385 -401.
23
[12] Z. Shiri, A. R. Ashrafi, Dependence polynomials of some graph operations,
24
Vietnam J. Math. 43 (2015) 755 - 769.
25
[13] D. B. West, Introduction to Graph Theory, Second Edition, Prentice Hall,
26
Inc., Upper Saddle River, NJ, 2001.
27
ORIGINAL_ARTICLE
A Mathematical Model for Evaluating the Efficiency of the University of Kashan’s Faculties
Efficiency evaluation of units has been of interest since many years in different domains such as management, economy, business, banking, and many others. Data envelopment analysis is one of the popular operations research methods for measuring the relative efficiency of units, which use multiple inputs to produce multiple outputs. As we know, universities play a key role in many aspects of a country such as industry, economic, training and many others. Therefore, evaluating the efficiency of the departments of a specific university is vital for effective allocation and utilization of educational resources, and consequently for enhancing its overall performance. In this paper, we try to identify teaching and research strengths and weaknesses of each department of university of Kashan and to provide a powerful tool for a fair comparison. To do this, we first determine the effective input and output variables for each teaching and research components. We then present a DEA model to evaluate both relative teaching and research efficiencies of each department of university of Kashan.
https://mir.kashanu.ac.ir/article_49257_4c1a0f73c44d0062e5a482a276514d80.pdf
2020-03-01
23
32
10.22052/mir.2017.89450.1066
Data Envelopment Analysis
Efficiency measurement
department's efficiency
Mostafa
Davtalab-Olyaie
mostafaolyaie62@gmail.com
1
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
LEAD_AUTHOR
Saeed
Maleki
mohammadsaeed21555@yahoo.com
2
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
AUTHOR
[1] M. Abbott and C. Doucouliagos, The efficiency of Australian universities: a data envelopment analysis, Economics of Education Review 22 (2003) 89–97.
1
[2] N. K. Avkiran, Investigating technical and scale efficiencies of Australian Universities through data envelopment analysis, Socio-Economic Planning Sciences 35 (2001) 57–80.
2
[3] R. D. Banker, A. Charnes and W. W. Cooper, Some methods for estimating technical and scale inefficiencies in data envelopment analysis, Management Science 30 (1984) 1078–1092.
3
[4] J. E. Beasley, Determining teaching and research efficiencies, Journal of the Operational Research Society 46 (1995) 441–452.
4
[5] M. L. Bougnol and J. H. Dulá, Validating DEA as a ranking tool: an application of DEA to assess performance in higher education, Ann. Oper. Res. 145 (2006) 339–365.
5
[6] T. M. Breu and R. L. Raab, Efficiency and perceived quality of the nation’s "top 25" National Universities and National Liberal Arts Colleges: An application of data envelopment analysis to higher education, Socio-Economic Planning Sciences 28 (1994) 33–45.
6
[7] A. Charnes, W. W. Cooper and E. Rhodes, Measuring the efficiency of decision making units, European J. Oper. Res. 2 (1978) 429–444.
7
[8] W. D. Cook, M. Hababou and H. J. H. Tuenter, Multicomponent efficiency measurement and shared inputs in data envelopment analysis: An application to sales and service performance in bank branches, Journal of Productivity Analysis 14 (2000) 209–224.
8
[9] W. D. Cook and L. M. Seiford, Data envelopment analysis (DEA) – Thirty years on, European J. Oper. Res. 192 (2009) 1–17.
9
[10] W. W. Cooper, L. M. Seiford and K. Tone, Data Envelopment Analysis, A Comprehensive Text with Models, Applications, References and DEA-Solver Software, Springer US, Springer-Verlag US (2007).
10
[11] S. Gattoufi, M. Oral and A. Reisman, A taxonomy for data envelopment analysis, Socio-Economic Planning Sciences 38 (2004) 141–158.
11
[12] H. Izadi, G. Johnes, R. Oskrochi and R. Crouchley, Stochastic frontier estimation of a CES cost function: the case of higher education in Britain, Economics of Education Review 21 (2002) 63–71.
12
[13] J. Johnes and G. Johnes, Research funding and performance in U.K. University Departments of Economics: A frontier analysis, Economics of Education Review 14 (1995) 301–314.
13
[14] J. Johnes and L. Yu, Measuring the research performance of Chinese higher education institutions using data envelopment analysis, China Economic Review 19 (2008) 679–696.
14
[15] C. T. Kuah and K. Y. Wong, Efficiency assessment of universities through data envelopment analysis, Procedia Computer Science 3 (2011) 499–506.
15
[16] C. T. Kuah, K. Y. Wong and F. Behrouzi, A review on data envelopment analysis (DEA), Fourth Asia International Conference on Mathematical/Analytical Modelling and Computer Simulation, pp. 168–173, Kota Kinabalu, Malaysia, Malaysia, 2010.
16
[17] Z. Sinuany-Stern, A. Mehrez and A. Barboy, Academic departments efficiency via DEA, Computers & Operations Research 21 (1994) 543–556.
17
ORIGINAL_ARTICLE
Structure of the Fixed Point of Condensing Set-Valued Maps
In this paper, we present structure of the fixed point set results for condensing set-valued map. Also, we prove a generalization of the Krasnosel'skii-Perov connectedness principle to the case of condensing set-valued maps.
https://mir.kashanu.ac.ir/article_54828_a3a52a4223907b65fdd6d42909995c7c.pdf
2020-03-01
33
41
10.22052/mir.2017.95130.1072
fixed point
condensing map
degree theory
Zeinab
Soltani
z.soltani@kashanu.ac.ir
1
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, 87317-53153, Iran
LEAD_AUTHOR
[1] F. E. Browder, A further generalization of the Schauder fixed point theorem, Duke Math. J. 32 (1965) 575–578.
1
[2] D. Bugajewski, Weak solutions of integral equations with weakly singular kernel in Banach spaces, Comment. Math. (Prace Mat.) 34 (1994) 49–58.
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[3] G. Darbo, Punti uniti in transformazioni a condiminio non compatto, Rend. Sem. Math. Univ. Padova. 24 (1955) 84–92.
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[4] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin – Heidelberg, 1985.
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[5] J. Dugundji and A. Granas, Fixed Point Theory, Volume 1, Serie, Monografie Matematyczne, PWN, Warsaw 1982.
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[6] M. Fakhar, Z. Soltani and J. Zafarani, The Lefschetz fixed point theorem and its application to asymptotic fixed point theorem for set-valued mappings, J. Fixed Point Theory Appl. 17 (2015) 287–300.
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[7] B. D. Gel’man, Topological properties of the set of fixed points of a multivalued map, Sb. Math. 188(12) (1997) 1761-1782.
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[8] L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Springer, New York, USA, 2006.
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[9] M. A. Krasnosel’ski and A. I. Perov, On the existence of solutions of certain non-linear operator equations, Dokl. Akad. Nauk. SSSR 126 (1959) 15–18.
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[11] T. W. Ma, Topological degrees of set-valued compact vector fields in locally convex spaces, Dissertiones Math. Rozprawy Mat. 92 (1972) 1–43.
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[12] J. Mallet-Paret and R. D. Nussbaum, Asymptotic fixed point theory and the beer barrel theorem, J. Fixed Point Theory Appl. 4 (2008) 203–245.
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[14] W. V. Petryshyn and P. M. Fitzpatrick, A degree theory, fixed point theorems, and mapping theorems for multivalued noncompact mappings, Trans. Amer. Math. Soc. 194 (1974) 1–25.
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[15] B. N. Sadovski˘ı, On a fixed point principle, (Russian) Funkcional. Anal. i Priložen. 1 (1967) 74–76.
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[16] J. Schauder, Der fixpunktsatz in funktionalräumen, Studia Math. 2 (1930) 171–180.
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[17] V. Seda, A remark to the schauder fixed point theorem, Dedicated to Juliusz Schauder, 1899?1943, Topol. Methods Nonlinear Anal. 15 (2000) 61–73.
17
ORIGINAL_ARTICLE
On the Estrada Index of Seidel Matrix
Let G be a simple graph with n vertices and with the Seidel matrix S. Suppose μ1, μ2,..., μn are the Seidel eigenvalues of G. The Estrada index of the Seidel matrix of G is defined as SEE(G)=\sum_{i=1}^{n} eμi. In this paper, we compute the Estrada index of the Seidel matrix of some known graphs. Also, some bounds for the Seidel energy of graphs are given.
https://mir.kashanu.ac.ir/article_107699_6cdacbe1cea3da68282ce63081336193.pdf
2020-03-01
43
54
10.22052/mir.2019.179267.1128
Seidel matrix
Seidel eigenvalue
Estrada index
Mardjan
Hakimi-Nezhaad
m.hakimi20@gmail.com
1
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran
AUTHOR
Modjtaba
Ghorbani
ghorbani30@gmail.com
2
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran
LEAD_AUTHOR
[1] T. Aleksić, I. Gutman and M. Petrović, Estrada index of iterated line graphs, Bull. Cl. Sci. Math. Nat. Sci. Math. 134 (2007) 33 − 41.
1
[2] J. Askari, A. Iranmanesh and K. C. Das, Seidel-Estrada index, J. Inequal. Appl. (2016) 120, 9 pp.
2
[3] N. Biggs, Algebraic Graph Theory, Cambridge University Press, Cambridge, 1993.
3
[4] A. E. Brouwer and W. H. Haemers, Spectra of Graphs, Universitext, Springer, New York, 2012.
4
[5] J. A. De la Pe˜ na, I. Gutman and J. Rada, Estimating the Estrada index, Linear Algebra Appl. 427 (2007) 70 − 76.
5
[6] E. Estrada, Characterization of 3D molecular structure, Chem. Phys. Lett. 319 (2000) 713 – 718.
6
[7] E. Estrada, Characterization of the folding degree of proteins, Bioinformatics 18 (2002) 697 − 704.
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[8] E. Estrada and J. A. Rodríguez-Velázquez, Subgraph centrality in complex networks, Phys. Rev. E 71 (5) (2005) 056103, 9 pp.
8
[9] E. Estrada, Topological structural classes of complex networks, Phys. Rev. E 75 (2007) 016103.
9
[10] M. Ghorbani, On the energy and Estrada index of Cayley graphs, Discrete Math. Algorithms Appl. 7 (1) (2015) 1550005, 8 pp.
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[11] M. Ghorbani and E. Bani-Asadi, On the Estrada and Laplacian Estrada In-dices of Fullerenes, J. Comput. Theor. Nanosci. 12 (6) (2015) 1064 − 1068.
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[12] G. Greaves, J. H. Koolen, A. Munemasa and F. Szöllősi, Equiangular lines in Euclidean spaces, J. Combin. Theory Ser. A 138 (2016) 208 − 235.
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[13] W. H. Haemers and G. R. Omidi, Universal adjacency matrices with two eigenvalues, Linear Algebra Appl. 435 (10) (2011) 2520 − 2529.
13
[14] W. H. Haemers, Seidel switching and graph energy, MATCH Commun. Math. Comput. Chem. 68 (3) (2012) 653 − 659.
14
[15] M. Hakimi-Nezhaad, H. Hua, A. R Ashrafi and S. Qian, The normalized Laplacian Estrada index of graphs, J. Appl. Math. Inform. 32 (1-2) (2014) 227 − 245.
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[16] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univer-sity Press, Cambridge, 1988.
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[17] H. S. Ramane, M. M. Gundloor and S. M. Hosamani, Seidel equienergetic graphs, Bull. Math. Sci. Appl. 16 (2016) 62 − 69.
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[18] R. Todeschini and V. Consonni, Handbook of Molecular Descriptors, Wiley-VCH, Weinheim, 2000.
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[19] J. H. van Lint and J. J. Seidel, Equilateral point sets in elliptic geometry, Proc. KNAW A 69; Indag. Math. 28 (1966) 335 − 348.
19
ORIGINAL_ARTICLE
Random Walk Modeling for Retrieving Information on Semantic Networking
In this article, the famous random walk model is exploited as a model of stochastic processes to retrieve some specific words which are used in social media by users. By spreading activation on semantic networking, this model can predict the probability of the words' activation, including all probabilities in different steps. In fact, the trend of probability in different steps is shown and the result of two different weights, when the steps tend to infinity is compared. In addition, it is shown that the results of the random walk model are aligned with the experimental psychological tests, showing that, as a model for semantic memory, it is a suitable model for retrieving in social media.
https://mir.kashanu.ac.ir/article_107700_0dbfd67b46a87677d04d1457247bba15.pdf
2020-03-01
55
70
10.22052/mir.2020.210794.1186
Semantic networking
Retrieval system
Random walk model
Spreading activation
Social Media
Meghdad
Abarghouei Nejad
meghdad.abarghouei.nejad@gmail.com
1
Department of computational cognitive modeling, Institute of cognitive science study, Tehran, Iran
AUTHOR
Azizollah
Memariani
salmanabar@gmail.com
2
Department of financial mathematic, kharazmi university, Tehran, Iran.
LEAD_AUTHOR
Javad
Hatami
hatamijm@gmail.com
3
University of Tehran,Institute for cognitive sciences studies
AUTHOR
Masoud
Asadpour
asadpour@gmail.com
4
Department of computational cognitive modeling, Institute of cognitive science study, Tehran, Iran.
AUTHOR
[1] R. Baeza-Yates and R. Ribeiro-Neto, Modern Information Retrieval, ACM Press / Addison Wesley, 1999.
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[3] Y. Campbell, A. W. Lo and A. C. MacKinlay, The Econometrics of Financial Markets, Princeton University Press, Princeton, NJ, USA, 1996.
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[5] N. Craswell and M. Szummer, Random Walks on the Click Graph, Proc. of SIGIR, 2007.
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[10] O. Häggström, Finite Markov Chains and Algorithmic Applications, Cambridge University Press, Cambridge, UK, 2002.
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and H. E. Stanley, Optimizing the success of random searches, Nature 401 (1999) 911 - 914.
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