@article {
author = {Gutman, Ivan and Furtula, Boris},
title = {Survey of Graph Energies},
journal = {Mathematics Interdisciplinary Research},
volume = {2},
number = {2},
pages = {85-129},
year = {2017},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2017.81507.1057},
abstract = {Let graph energy is a graph--spectrum--based quantity, introduced in the 1970s. After a latent period of 20--30 years, it became a popular topic of research both in mathematical chemistry and in ``pure'' spectral graph theory, resulting in over 600 published papers. Eventually, scores of different graph energies have been conceived. In this article we provide the basic facts on graph energies, in particular historical and bibliographic data.},
keywords = {Energy,spectrum,Graph},
url = {http://mir.kashanu.ac.ir/article_46658.html},
eprint = {http://mir.kashanu.ac.ir/article_46658_d162c1bd23ebd5a2f91d1be3caf51c63.pdf}
}
@article {
author = {De, Nilanjan},
title = {On Eccentricity Version of Laplacian Energy of a Graph},
journal = {Mathematics Interdisciplinary Research},
volume = {2},
number = {2},
pages = {131-139},
year = {2017},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2017.70534.1051},
abstract = {The energy of a graph G is equal to the sum of absolute values of the eigenvalues of the adjacency matrix of G, whereas the Laplacian energy of a graph G is equal to the sum of the absolute value of the difference between the eigenvalues of the Laplacian matrix of G and the average degree of the vertices of G. Motivated by the work from Sharafdini and Panahbar [R. Sharafdini, H. Panahbar, Vertex weighted Laplacian graph energy and other topological indices. J. Math. Nanosci. 2016, 6, 57-65], in this paper we investigate the eccentricity version of Laplacian energy of a graph G.},
keywords = {Eccentricity,Eigenvalue,energy (of graph),Laplacian energy,topological index},
url = {http://mir.kashanu.ac.ir/article_46665.html},
eprint = {http://mir.kashanu.ac.ir/article_46665_5d4ef03c2a66934ca736a18abb23be5f.pdf}
}
@article {
author = {Milovanovic, Emina and Milovanovic, Igor and Matejic, Marjan},
title = {On Relation between the Kirchhoff Index and Laplacian-Energy-Like Invariant of Graphs},
journal = {Mathematics Interdisciplinary Research},
volume = {2},
number = {2},
pages = {141-154},
year = {2017},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2017.85687.1063},
abstract = {Let G be a simple connected graph with n ≤ 2 vertices and m edges, and let μ1 ≥ μ2 ≥...≥μn-1 >μn=0 be its Laplacian eigenvalues. The Kirchhoff index and Laplacian-energy-like invariant (LEL) of graph G are defined as Kf(G)=nΣi=1n-11/μi and LEL(G)=Σi=1n-1 √μi, respectively. In this paper we consider relationship between Kf(G) and LEL(G).},
keywords = {Kirchhoff index,Laplacian-energy-like invariant,Laplacian eigenvalues of graph},
url = {http://mir.kashanu.ac.ir/article_46678.html},
eprint = {http://mir.kashanu.ac.ir/article_46678_73d7cbf6e273d4d973106287024507a7.pdf}
}
@article {
author = {Ellahi, Hamid Reza and Nasiri, Ramin and Fath-Tabar, Gholam Hossein and Gholami, Ahmad},
title = {The Signless Laplacian Estrada Index of Unicyclic Graphs},
journal = {Mathematics Interdisciplinary Research},
volume = {2},
number = {2},
pages = {155-167},
year = {2017},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2017.57775.1038},
abstract = {For a simple graph $G$, the signless Laplacian Estrada index is defined as $SLEE(G)=\sum^{n}_{i=1}e^{q^{}_i}$, where $q^{}_1, q^{}_2, \dots, q^{}_n$ are the eigenvalues of the signless Laplacian matrix of $G$. In this paper, we first characterize the unicyclic graphs with the first two largest and smallest $SLEE$'s and then determine the unique unicyclic graph with maximum $SLEE$ among all unicyclic graphs on $n$ vertices with a given diameter. All extremal graphs, which have been introduced in our results are also extremal with respect to the signless Laplacian resolvent energy.},
keywords = {Signless Laplacian Estrada index,unicyclic graphs,extremal graphs,diameter,signless Laplacian resolvent energy},
url = {http://mir.kashanu.ac.ir/article_46679.html},
eprint = {http://mir.kashanu.ac.ir/article_46679_9ebe519f917a721f6f9fd832c72a83d7.pdf}
}
@article {
author = {Ramane, Harishchandra S. and Gundloor, Mahadevappa M.},
title = {More Equienergetic Signed Graphs},
journal = {Mathematics Interdisciplinary Research},
volume = {2},
number = {2},
pages = {169-179},
year = {2017},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2017.90820.1068},
abstract = {The energy of signed graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Two signed graphs are said to be equienergetic if they have same energy. In the literature the construction of equienergetic signed graphs are reported. In this paper we obtain the characteristic polynomial and energy of the join of two signed graphs and thereby we give another construction of unbalanced, noncospectral equieneregtic signed graphs on $n geq 8$ vertices.},
keywords = {Signed graph,energy of a graph,equienergetic graphs},
url = {http://mir.kashanu.ac.ir/article_49308.html},
eprint = {http://mir.kashanu.ac.ir/article_49308_3be7bf0a0c2de6562035165081ffbebc.pdf}
}
@article {
author = {Ramane, Harishchandra and Gutman, Ivan and Patil, Jayashri and Jummannaver, Raju},
title = {Seidel Signless Laplacian Energy of Graphs},
journal = {Mathematics Interdisciplinary Research},
volume = {2},
number = {2},
pages = {181-191},
year = {2017},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2017.101641.1081},
abstract = {Let $S(G)$ be the Seidel matrix of a graph $G$ of order $n$ and let $D_S(G)=diag(n-1-2d_1, n-1-2d_2,\ldots, n-1-2d_n)$ be the diagonal matrix with $d_i$ denoting the degree of a vertex $v_i$ in $G$. The Seidel Laplacian matrix of $G$ is defined as $SL(G)=D_S(G)-S(G)$ and the Seidel signless Laplacian matrix as $SL^+(G)=D_S(G)+S(G)$. The Seidel signless Laplacian energy $E_{SL^+}(G)$ is defined as the sum of the absolute deviations of the eigenvalues of $SL^+(G)$ from their mean. In this paper, we establish the main properties of the eigenvalues of $SL^+(G)$ and of $E_{SL^+}(G)$.},
keywords = {Seidel Laplacian eigenvalues,Seidel Laplacian energy,Seidel signless Laplacian matrix,Seidel signless Laplacian eigenvalues,Seidel signless Laplacian energy},
url = {http://mir.kashanu.ac.ir/article_53998.html},
eprint = {http://mir.kashanu.ac.ir/article_53998_01ab0ae77936bf1f5161db2349204526.pdf}
}
@article {
author = {Jalali-Rad, Maryam},
title = {Eigenvalues of the Cayley Graph of Some Groups with respect to a Normal Subset},
journal = {Mathematics Interdisciplinary Research},
volume = {2},
number = {2},
pages = {193-207},
year = {2017},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2017.101675.1082},
abstract = {Set X = { M11, M12, M22, M23, M24, Zn, T4n, SD8n, Sz(q), G2(q), V8n}, where M11, M12, M22, M23, M24 are Mathieu groups and Zn, T4n, SD8n, Sz(q), G2(q) and V8n denote the cyclic, dicyclic, semi-dihedral, Suzuki, Ree and a group of order 8n presented by V8n = < a, b | a^{2n} = b^{4} = e, aba = b^{-1}, ab^{-1}a = b>,respectively. In this paper, we compute all eigenvalues of Cay(G,T), where G \in X and T is minimal, second minimal, maximal or second maximal normal subset of G\{e} with respect to its size. In the case that S is a minimal normal subset of G\{e}, the summation of the absolute value of eigenvalues, energy of the Cayley graph, are evaluated.},
keywords = {Simple group,Cayley graph,eigenvalue,energy},
url = {http://mir.kashanu.ac.ir/article_53999.html},
eprint = {http://mir.kashanu.ac.ir/article_53999_50a22096d7b267c4ef41bd53e9f89c1e.pdf}
}
@article {
author = {Sharada, Biligirirangaiah and Sowaity, Mohammad Issa and Gutman, Ivan},
title = {Laplacian Sum-Eccentricity Energy of a Graph},
journal = {Mathematics Interdisciplinary Research},
volume = {2},
number = {2},
pages = {209-219},
year = {2017},
publisher = {University of Kashan},
issn = {2538-3639},
eissn = {2476-4965},
doi = {10.22052/mir.2017.106176.1084},
abstract = {We introduce the Laplacian sum-eccentricity matrix LS_e} of a graph G, and its Laplacian sum-eccentricity energy LS_eE=\sum_{i=1}^n |\eta_i|, where \eta_i=\zeta_i-\frac{2m}{n} and where \zeta_1,\zeta_2,\ldots,\zeta_n are the eigenvalues of LS_e}. Upper bounds for LS_eE are obtained. A graph is said to be twinenergetic if \sum_{i=1}^n |\eta_i|=\sum_{i=1}^n |\zeta_i|. Conditions for the existence of such graphs are established.},
keywords = {Sum-eccentricity eigenvalues,sum-eccentricity energy,Laplacian sum-eccentricity matrix,Laplacian sum-eccentricity energy},
url = {http://mir.kashanu.ac.ir/article_54000.html},
eprint = {http://mir.kashanu.ac.ir/article_54000_a60755aff16ea35f3f068051c0878426.pdf}
}