Exponential fraction index of certain graphs

Topological indices play a great role in Mathematical chemistry. Many graph theorists as well as chemists attracted towards these molecular descriptors. The aim of this paper is to introduce and investigate the Exponential Fraction index (a degree based Topological index). It is defined as follows. EF(G) = Σ uv∈E(G) edu/dv . Here du and dv are the maximum and minimum degree respectively. In this paper, we calculate the Exponential Fraction index of double graphs, subdivision graphs and complements of some standard graphs. Also we compute the index for chemical structures Graphene and Carbon nanocones.Publisher's Versio

Maximum and minimum degree energies of p-splitting and p-shadow graphs

Let vi and vj be two vertices of a graph G. The maximum degree matrix of G is given in [2] by dij = {max {di, dj} if vi and vj are adjacent 0 otherwise. Similarly the (i, j)-th entry of the minimum degree matrix is defined by taking the minimum degree instead of the maximum degree above, [1]. In this paper, we have elucidated a relation between maximum degree energy of p−shadow graphs with the maximum degree energy of its underlying graph. Similarly, a relation has been derived for minimum degree energy also. We disprove the results EM(S0 (G)) = 2EM(G) and Em(S0 (G)) = 2Em(G) given by Zheng-Qing Chu et al. [3] by giving some counterexamples.Publisher's Versio