On the First and Second Locating Zagreb Indices of Graphs

Abstract

By the distance or degree of vertices of the molecular graph, we can define graph invariant called topological indices. Which are used in chemical graph to describe the structures and predicting some physicochemical properties of chemical compound? In this paper, by introducing two new topological indices under the name first and second Zagreb locating indices of a graph G, we establish the exact values of those indices for some standard families of graphs included the firefly graph.

The Edge-Weighted Graph Entropy Using Redefined Zagreb Indices

“…Few of them are first and second Zagreb indices M 1 (G) and M 2 (G), respectively, exhibiting applicability for deriving multi-linear regression models. Details on the chemical applications of these indices can be seen in [25,26]. More results on Zagreb indices can be seen in [27,28].…”

Locating and Multiplicative Locating Indices of Graphs with QSPR Analysis

“…[18,19]). Moreover, in a recent work, Wazzan et al (see [20]) introduced novel topological indices called the first and second locating indices. To do that, the authors used the locating matrix Lo(G) over a graph G (cf.…”

“…is the distance between the vertices v i and v j in G. e vector v i → is called the locating vector corresponding to the vertex v i , where v i → • v j → is actually the dot product of the vectors v i → and v j → in the integers space Z + ∪ 0 { } such that v i is adjacent to v j . In the present paper, as a next step of the work in [20], we introduce the first and second multiplicative locating indices for a connected graph G as in the following definition. Definition 1.…”

Domination topological properties of polyhydroxybutyrate and polycaprolactone with QSPR analysis

“…Topological indices are the numerical parameters of a graph, and these parameters are the same for graphs which are isomorphic. A variety of topological indices have been created and developed, and many studies have been conducted on them in various fields of molecular graphs and networks [9][10][11][12][13][14]. A. M. Hanan Ahmed et al [15], have introduced new degree-based topological indices called domination topological indices which are based on the minimal dominating sets.…”