let $g$ be a connected graph of order $3$ or more and $c:e(g)rightarrowmathbb{z}_k$‎ ‎($kge 2$) a $k$-edge coloring of $g$ where adjacent edges may be colored the same‎. ‎the color sum $s(v)$ of a vertex $v$ of $g$ is the sum in $mathbb{z}_k$ of the colors of the edges incident with $v.$ the $k$-edge coloring $c$ is a modular $k$-edge coloring of $g$ if $s(u)ne s(v)$ in $mathbb{z}_k$ for all pa...

Let $G$ be a simple connected graph. In this paper, Szeged dimension and PI$_v$ dimension of graph $G$ are introduced. It is proved that if $G$ is a graph of Szeged dimension $1$ then line graph of $G$ is 2-connected. The dimensions of five composite graphs: sum, corona, composition, disjunction and symmetric difference with strongly regular components is computed. Also explicit formulas of Sze...

function f: G  , with this property that f(G1) = f(G2) if G1 and G2 are isomorphic. There are several vertex distance-based and degree-based indices which introduced to analyze the chemical properties of molecule graph. For instance: Wiener index, PI index, Szeged index, geometric-arithmetic index, atom-bond connectivity index and general sum connectivity index are introduced to test the perf...

The Szeged index (Sz) is a recently proposed1q2 structural descriptor, based on the distances of the vertices of the molecular graph. In order to be able to study the properties of this novel topological index it would be advantageous to possess an easy method for its calculation. The calculation of Sz directly from its definition (see below) is quite cumbersome, especially in the case of large...

Let G= V E be a simple connected graph. The distance between two vertices of G is defined to be the length of the shortest path between the two vertices. There are topological indices assigned to G and based on the distance function which are invariant under the action of the automorphism group of G. Some important indices assigned to G are the Wiener, Szeged, and PI index which we will find th...

The mathematical properties of nano molecules are an interesting branch of nanoscience for researches nowadays. The periodic open single wall tubulene is one of the nano molecules which is built up from two caps and a distancing nanotube/neck. We discuss how to automatically construct the graph of this molecule and plot the graph by spring layout algorithm in graphviz and netwrokx packages. The...

a Department of Inorganic and Analytical Chemistry, University of Szeged, Dóm tér 7. H-6720 Szeged, Hungary 8 b MTA-SZTE Bioinorganic Chemistry Research Group, University of Szeged, Dóm tér 7. H-6720 Szeged, 9 Hungary 10 c Centro de Química e Bioquímica (CQB), Faculdade de Ciências, ULisboa, Campo Grande, Lisbon, Portugal 11 d Centro de Química Estrutural (CQE), Faculdade de Ciências, ULisboa, ...