2022-05-20T15:28:00Z https://mir.kashanu.ac.ir/?_action=export&rf=summon&issue=5243
2017-12-01 10.22052
Mathematics Interdisciplinary Research Math. Interdisc. Res. 2538-3639 2538-3639 2017 2 2 Survey of Graph Energies Ivan Gutman Boris Furtula 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.‎ Energy spectrum Graph 2017 12 01 85 129 https://mir.kashanu.ac.ir/article_46658_d162c1bd23ebd5a2f91d1be3caf51c63.pdf
2017-12-01 10.22052
Mathematics Interdisciplinary Research Math. Interdisc. Res. 2538-3639 2538-3639 2017 2 2 On Eccentricity Version of Laplacian Energy of a Graph Nilanjan De 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. Eccentricity Eigenvalue energy (of graph) Laplacian energy topological index 2017 12 01 131 139 https://mir.kashanu.ac.ir/article_46665_5d4ef03c2a66934ca736a18abb23be5f.pdf
2017-12-01 10.22052
Mathematics Interdisciplinary Research Math. Interdisc. Res. 2538-3639 2538-3639 2017 2 2 On Relation between the Kirchhoff Index and Laplacian-Energy-Like Invariant of Graphs Emina Milovanovic Igor Milovanovic Marjan Matejic 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). Kirchhoff index Laplacian-energy-like invariant Laplacian eigenvalues of graph 2017 12 01 141 154 https://mir.kashanu.ac.ir/article_46678_73d7cbf6e273d4d973106287024507a7.pdf
2017-12-01 10.22052
Mathematics Interdisciplinary Research Math. Interdisc. Res. 2538-3639 2538-3639 2017 2 2 The Signless Laplacian Estrada Index of Unicyclic Graphs Hamid Reza Ellahi Ramin Nasiri Gholam Hossein Fath-Tabar Ahmad Gholami ‎For a simple graph G‎, ‎the signless Laplacian Estrada index is defined as SLEE(G)=∑ni=1eqi‎, ‎where q1‎, ‎q2‎,...‎, ‎qn 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. ‎Signless Laplacian Estrada index‎ Unicyclic graphs‎ ‎extremal graphs‎ ‎diameter ‎signless Laplacian resolvent energy‎ 2017 12 01 155 167 https://mir.kashanu.ac.ir/article_46679_9ebe519f917a721f6f9fd832c72a83d7.pdf
2017-12-01 10.22052
Mathematics Interdisciplinary Research Math. Interdisc. Res. 2538-3639 2538-3639 2017 2 2 More Equienergetic Signed Graphs Harishchandra S. ‎Ramane Mahadevappa M. Gundloor 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 ≥ 8 vertices. Signed graph energy of a graph equienergetic graphs 2017 12 01 169 179 https://mir.kashanu.ac.ir/article_49308_3be7bf0a0c2de6562035165081ffbebc.pdf
2017-12-01 10.22052
Mathematics Interdisciplinary Research Math. Interdisc. Res. 2538-3639 2538-3639 2017 2 2 Seidel Signless Laplacian Energy of Graphs Harishchandra Ramane Ivan Gutman Jayashri Patil Raju Jummannaver Let S(G) be the Seidel matrix of a graph G of order n and let DS(G)=diag(n-1-2d1, n-1-2d2,..., n-1-2dn) 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)=DS(G)+S(G). The Seidel signless Laplacian energy ESL+(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 ESL+(G). Seidel Laplacian eigenvalues Seidel Laplacian energy Seidel signless Laplacian matrix Seidel signless Laplacian eigenvalues Seidel signless Laplacian energy 2017 12 01 181 191 https://mir.kashanu.ac.ir/article_53998_01ab0ae77936bf1f5161db2349204526.pdf
2017-12-01 10.22052
Mathematics Interdisciplinary Research Math. Interdisc. Res. 2538-3639 2538-3639 2017 2 2 Eigenvalues of the Cayley Graph of Some Groups with respect to a Normal Subset Maryam Jalali-Rad ‎‎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 | a2n = b4 = e‎, ‎ aba = b-1‎, ‎ab-1a = 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. Simple group‎ ‎Cayley graph‎ ‎eigenvalue‎ ‎energy 2017 12 01 193 207 https://mir.kashanu.ac.ir/article_53999_50a22096d7b267c4ef41bd53e9f89c1e.pdf
2017-12-01 10.22052
Mathematics Interdisciplinary Research Math. Interdisc. Res. 2538-3639 2538-3639 2017 2 2 Laplacian Sum-Eccentricity Energy of a Graph Biligirirangaiah Sharada Mohammad Issa Sowaity Ivan Gutman We introduce the Laplacian sum-eccentricity matrix LSe of a graph G, and its Laplacian sum-eccentricity energy LSeE=∑ni=1|ηi|, where ηi=ξi-(2m/n) and where ξ1,ξ2,...,ξn are the eigenvalues of LSe. Upper bounds for LSeE are obtained. A graph is said to be twinenergetic if ∑ni=1|ηi|=∑ni=1|ξi|. Conditions for the existence of such graphs are established. Sum-eccentricity eigenvalues sum-eccentricity energy Laplacian sum-eccentricity matrix Laplacian sum-eccentricity energy 2017 12 01 209 219 https://mir.kashanu.ac.ir/article_54000_a60755aff16ea35f3f068051c0878426.pdf