﻿ Marjan Matejic

Marjan Matejic

Faculty of Electronic Engineering, University of Nis, Nis, Serbia

[ 1 ] - On Relation between the Kirchhoff Index and Laplacian-Energy-Like Invariant of Graphs

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-1<...

[ 2 ] - Some new bounds on the general sum--connectivity index

Let \$G=(V,E)\$ be a simple connectedgraph with \$n\$ vertices, \$m\$ edges and sequence of vertex degrees\$d_1 ge d_2 ge cdots ge d_n>0\$, \$d_i=d(v_i)\$, where \$v_iin V\$. With \$isim j\$ we denote adjacency ofvertices \$v_i\$ and \$v_j\$. The generalsum--connectivity index of graph is defined as \$chi_{alpha}(G)=sum_{isim j}(d_i+d_j)^{alpha}\$, where \$alpha\$ is an arbitrary real<b...

[ 3 ] - A note on the first Zagreb index and coindex of graphs

Let \$G=(V,E)\$, \$V={v_1,v_2,ldots,v_n}\$, be a simple graph with\$n\$ vertices, \$m\$ edges and a sequence of vertex degrees\$Delta=d_1ge d_2ge cdots ge d_n=delta\$, \$d_i=d(v_i)\$. Ifvertices \$v_i\$ and \$v_j\$ are adjacent in \$G\$, it is denoted as \$isim j\$, otherwise, we write \$insim j\$. The first Zagreb index isvertex-degree-based graph invariant defined as\$M_1(G)=sum_{i=1}^nd_i^2\$, whereas the first Zag...

[ 4 ] - Some remarks on the sum of the inverse values of the normalized signless Laplacian eigenvalues of graphs

Let G=(V,E), \$V={v_1,v_2,ldots,v_n}\$, be a simple connected graph with \$%n\$ vertices, \$m\$ edges and a sequence of vertex degrees \$d_1geqd_2geqcdotsgeq d_n>0\$, \$d_i=d(v_i)\$. Let \${A}=(a_{ij})_{ntimes n}\$ and \${%D}=mathrm{diag }(d_1,d_2,ldots , d_n)\$ be the adjacency and the diagonaldegree matrix of \$G\$, respectively. Denote by \${mathcal{L}^+}(G)={D}^{-1/2}(D+A) {D}^{-1/2}\$ the normalized signles...

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