Reformulated Reciprocal Degree Distance Index And The Forcing Numbers Of Maximum Matchings In Aromatic Hexagonal Chains

The topological index of chemical molecule is a kind of numerical invariant,which can predict indirectly the physical and chemical properties of the corresponding chemical.The reformulated reciprocal degree distance index is a generalized of reciprocal degree distance,defined as:Rt(G=(?)dG(u)+dG(v)/dG(u,v),t?0[1].Phenylene chain and spiro hexagonal chain are two kinds of important aromatic chemical molecule,which have strongly chemical background.The first part of the paper study the reformulated reciprocal degree distance index of phenylene chains.Let M be a maximum matching of a graph G,and S be a subset of M,if S forces the unique maximum matching M and occurs simultaneously in no other maximum matchings,such an S is called a forcing set of M.The minimum cardinality of the forcing number of M,written by fM(G,M).The minimum value of the forcing numbers of all maximum matchings in G is called the minimum forcing number of G,denoted by fM(G).The second part of the paper study the forcing numbers of maximum matchings of some special graphs.The paper is divided into three chapters.In chapter 1,we first introduce the definitions and notations used in the paper,Secondly,we present main results of this paper.In chapter 2,we mainly study the reformulated reciprocal degree distance index of phenylene chain,and present extremum phenylene chains with maximum minimum refor-mulated reciprocal degree distance index.In chapter 3,we consider the forcing sets of some special graphs,and present the forcing number of maximum matching of spiro hexagonal para-chains and five classes of special graphs.