Some Topological Indices Of(Generalized)Mycielskian Of Graphs And Its Complement

Viewing the carbon atoms of the chemical molecule as the vertices,and the bonds between the carbon atoms as the edges between the corresponding points,we can get the carbon atoms skeleton diagram of the chemical molecule.The numerical invariant(namely topological indices)defined on the carbon atoms skele-ton diagram of the chemical molecule,is numerical descriptors that allow the numerical characterization of chemical molecule structures.By exploring various topological indices of carbon atoms skeleton diagram to chemical molecule,the physical and chemical and chemical properties of the corresponding chemical can be predicted indirectly.Such as:boiling point,stability and energy etc.In a search for triangle-free with arbitrarily large chromatic numbers,Mycielski devel-oped a graph transformation that transforms a graph G into a new graph ?(G),called the Mycielskian of G.The generalized Mycielskian ?k(G)(k?0),is a nature generalized of Mycielskian.The paper mainly studies the relationship of topological indices in(generalized)Myciel-skian graph and its complement.The paper is divided into five chapters.In the first chapter,we first introduce the defini-tions and notations used in the paper.Secondly,we present main results of this paper.In chapter2,we study the generalized Zagreb indices of(generalized)Mycielskian graph and its complement,which can be viewed as generalized of results in Theorem3.3 in litera-ture[2].In chapter3,according to some parameters of G,such as:order of G,size of G,M1(G)and M2(G),we present the exact value of Wiener indices of Mycielskian graph and its complement.In chapter4,we present the exact value of Gutman indices of Mycielskian graph and its complement in terms of order of G,size of G,M1(G)and M2(G).In chapter5,the Szeged indices of Mycielskian graph of G and its complement presented in terms of order of G,size of G,M1(G)and M2(G).