Graph Energies of Generalized Chain on Petersen Graphs

Abstract

. The upper and lower bound of graph energy with minimal and maximal energy is abroad field of Spectral Graph theory. The energy of Graph E(G) in term of vertices and number of edges in graph G is involved in absolute value of eigen value adjacency matrix of G where l is the spectral radius. The Graph has energy equal toFinally, we determine the energy, pattern and irregularities of chain like Petersen Graph. Our exploring outputs will rely upon Size and Order of Graph, Degree of Graph, Irregular Graph, Multi Graph, Cyclic Graph, Bridge Graph, Connected and Planarity Graph, and Concept of Distance and Degree in Graph.We will construct linear functionals obtained from the differences of integral inequalities involving multidimensional monotone func- tions and give the log-convexity of these functionals using classical log-convexity method by cosidering a family of convex functions. At the end we will formulate Cauchy means for these functionals, using as an application of mean value theorems of Langrange and Cauchy type and deduce their monotonicity.