Topological Indices Of Cartesian Products Of Some Classes Of Graphs

Graph theory is the study of objects and relationships among them with the char-acteristics and properties.Using the knowledge of graph theory we can solve many practical problems associated with life,such as the famous Konigsberg seven Bridges problem,polyhedron of euler's theorem,the four color problem,etc in history.In QSAR/QSPR research we often use the topological index such as Randi(?) index,harmonic index,atom-bondconnectivity index and Geometric-arithmetic index,etc to predict the biological activity of chemical compounds.In fact,topological index is some val-ues which generated by transforming the chemical structure of the compounds.These topological index affect certain physical and chemical properties of chemicals such as boiling point,stability,and so on.In this article we mainly discuss the topological indices of Sierpi(?)ski graph,the cartesian products of wheel and fan and path.The full text is divided into five parts.In the first part,we briefly introduce the research background,definitions,struc-ture and main conclusion of the paper.In the second part,we present some basic concepts,symbol marks and related preliminary knowledge needed in the proof.In the third part,we mainly study the topological indices of Sierpi(?)ski graph.We first show that some basic characteristics of the vertices in Sierpi(?)ski graph,according to the characteristics of the vertex degree sequence,we can calculate the topo-logical indices of Sierpi(?)ski graph with any number of vertices,such as the general Randi(?) index,harmonic index,atom-bondconnectivity index,Geometric-arithmetic index.In the forth part,we consider the topological indices of graph operations.In this part,we obtain the topological indices of the cartesian products of wheel W_nand path P_m,wheel W_nand fan F_m,wheel W_nand wheel W_mand obtain their exact values.In the fifth part,we get the conclusion and summary of this paper and outlook of the future.