Some New Results Of The Hexagonal Chain And Random Multiple Hexagonal Chain

A hexagonal system(or benzenoid system)is a 2-connected plana graph in which all inner faces are regular hexagons.The hexagonal system has a strong chemical application background,which is the natural mapping of the carbon atom skeleton of a class of benzene compounds with super stability.A hexagon system is called a hexagon chain if each hexagon adjacent to at most two hexagons[1].A random multiple hexagonal chain with m layers can be formed by the fusion m copies of linear hexagonal chains Ln.A subset S of E(G)is called a complete forcing set of G on which the restriction of any perfect matching M is a forcing set of M.The minimum cardinality of complete forcing sets of G is the complete forcing number of G,denoted by cf(G).The paper mainly studies the reformulated reciprocal sum-degree distance and the gen-eralized Zagreb index of hexagonal chain and the random multiple hexagonal chain,more-over,the complete forcing number of random multiple hexagonal chain are considered.The paper is devided into four chapters.In the first chapter,we first introduce the definitions and notations used in the paper.Secondly,we present main results of this paper.In the second chapter,in all hexagonal chains containing n hexagons,we present two extremum hexagonal chains with the maximum and minimum reformulated reciprocal sum-degree distances,respectively,and give the ranges of the reformulated reciprocal sum-degree distances of two kinds of extremum hexagonal chains.In the third chapter,we mainly studies the generalized Zagreb index of random multiple hexagonal chains,and present the expected values of generalized Zagreb index of random multiple hexagonal chains.In the fourth chapter,we consider the complete forcing set of random multiple hexag-onal chains,and present the exactly formula of the complete forcing number of random multiple hexagonal chains.