On Topological Indices Of Some Graph Operations

The physical and chemical properties of compounds have a closed relationship with their topology.Since Wiener index,the first topological index,was introduced by Harold Wiener in 1947,scientists introduced many topological indices,and applied them widely to physic-s,chemistry and other applied science.Since most topological indices of molecules can be represented by the parameters of the corresponding molecular graphs,graph theory becomes a natural and strong tool for the study of physical and chemical properties of molecules.Notice that the computation of the indices of complex molecular graph is very difficult.To overcome such difficulty,graph operations such as generalized hierarchical product,join,symmetric dif-ference,composition and disjunction are introduced.Considering the importance of extremal graph theory in the study of converse structure-property problems,this work studies the com-putation of some important chemical indices of some graph operations,and characterizes the some corresponding extremal graphs.The main results are listed as follows.2.In chapter 2,Theorem 2.1.2 presents an explicit expression of the y-Wiener index of Generalized hierarchical product.3.In chapter 3,Theorem 3.1.2 presents explicit expressions of the first and the second Zagreb indices of Generalized hierarchical product,which results in these two indices of four F-sum product graphs.4.In chapter 4,Theorem 4.2.1 presents formulas on the q-Wiener indices of join,Disjunc-tion symmetric difference and Composition.5.In chapter 5,Theorem 5.2.2 presents an upper bound for the additively weighted Harary index of graphs with connectivity 1 ? k ? n-2,and characterizes the extremal graphs.6.Theorem 5.2.3 presents an upper bound for the additively weighted Harary index of graphs with any given matching number,and characterizes the extremal graphs.