It was conjectured that for each simple graph G = (V , E) with n = |V (G)| vertices and m = |E(G)| edges, it holdsM2(G)/m ≥ M1(G)/n, whereM1 andM2 are the first and second Zagreb indices. Hansen and Vukičević proved that it is true for all chemical graphs and does not hold in general. Also the conjecture was proved for all trees, unicyclic graphs, and all bicyclic graphs except one class. In th...

Let G be a simple graph possessing n vertices and m edges. Let di be the degree of the i-th vertex of G , i = 1, . . . , n . The first Zagreb index M1 is the sum of d 2 i over all vertices of G . The second Zagreb index M2 is the sum di dj over pairs of adjacent vertices of G . In this paper we search for graph for which M1/n = M2/m , and show how numerous such graphs can be constructed. In add...

Topological indices (TIs) assign a numeric value to graph or molecular structure. Due their ability predict the physiochemical properties of graph, several TIs have been introduced and studied, mainly based on degree distance. For vertex v , maximum distance id="M2">v from any other in id="M3">G</m...

A new extension of the generalized topological indices (GTI) approach is carried out to represent “simple” and “composite” topological indices (TIs) in an unified way. This approach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randić connectivity indices are expressed by means of ...

Graph theory can be used to optimize interconnection network systems. The compatibility of such networks mainly depends on their topology. Topological indices may characterize the topology networks. In this work, we studied a symmetric ?? formed by ? time repetition process joining ? copies selected graph ? in way that corresponding vertices all are joined with each other new edge. symmetry is ...

New graph invariants, named exponential Zagreb indices, are introduced for more than one type of index. After that, in terms lists on equality results over special graphs presented as well some new bounds unicyclic, acyclic, and general obtained. Moreover, these invariants determined operations.