The Inverse Sum Indeg Index Of Some Composite Graphs

In 1955,in a search for triangle-free graphs with arbitrarily large chromatic num-ber,Mycielski[1]introduced an interesting graph transformation which transforms a graph G into a new graph,called the Mycielskian of G,denoted by ?(G).The general-ized Mycielskian graph is proposed by Lam et al.and it is a natural extension of?(G),denoted by ?m(G),where m is the number of layers,which is also called by Tardif[2]cones over graphs.The inverse sum indeg index of G is defined as ISI(G)=(?)which is very important descriptor of total surface area of octane iso-mers.Using the structure of Mycielskian graph,study the inverse sum indeg indices of(Generalized)Mycielskian graph and complement graph of Mycielskian graph.In addition,we give the upper and lower bounds of the inverse sum indeg indices of(edge,modified edge)corona graph and adjacent corona graph.The paper is divided into three chapters.In the first chapter,we firstly introduce some research background and development status of the degree distance indices of(generalized)Mycielskian graph and it's complement graph,and the inverse sum indeg indices of corona graphs.Secondly,some basic concepts,terms and symbols used in this paper are given.Finally,the main results of this paper are illustrated.In the second chapter,we study about the inverse sum indeg index of(generalized)Mycielskian graph and complement of Mycielskian graph.Using some parameters of the original graph G,such as the number of points,edges,M1(G)and M2(G)give the upper and lower bounds of the inverse sum indeg indices of these graphs.According to the structure of corona graph,by using some parameters of corona graph,such as the vertex degree of each vertex,M1(G)and M2(G),the upper and lower bounds of inverse sum indeg indices of(edge,modified edge)corona graph and adjacent corona graph are obtained.