The Hosoya index of a graph is defined as the total number of the matching of the graph. In this paper, the ordering of polygonal chains with respect to Hosoya index is characterized.
Let G be a graph that admits a perfect matching M.A forcing set S for a perfect matching M is a subset of M such that it is contained in no other perfect matchings of G.The cardinality of a forcing set of M with the s...Let G be a graph that admits a perfect matching M.A forcing set S for a perfect matching M is a subset of M such that it is contained in no other perfect matchings of G.The cardinality of a forcing set of M with the smallest size is called the forcing number of M,denoted by f(G,M).The forcing spectrum of G is defined as:Spec(G)={f(G,M)|M is a perfect matching of G}.In this paper,by applying the Ztransformation graph(resonance graph)we show that for any polyomino with perfect matchings and any even polygonal chain,their forcing spectra are integral intervals.Further we obtain some sharp bounds on maximum and minimum forcing numbers of hexagonal chains with given number of kinks.Forcing spectra of two extremal chains are determined.展开更多
基金Supported by the National Natural Science Foundation of China(10761008)the Scientific Research Foundation of the Education Department of Guangxi Province of China(201010LX471,201010LX495,201106LX595,201106LX608)the Natural Science Fund of Hechi University(2011YBZ-N003,2012YBZ-N004)
文摘The Hosoya index of a graph is defined as the total number of the matching of the graph. In this paper, the ordering of polygonal chains with respect to Hosoya index is characterized.
基金supported by the National Natural Science Foundation of China(Nos.11871256,11371180,11226286)。
文摘Let G be a graph that admits a perfect matching M.A forcing set S for a perfect matching M is a subset of M such that it is contained in no other perfect matchings of G.The cardinality of a forcing set of M with the smallest size is called the forcing number of M,denoted by f(G,M).The forcing spectrum of G is defined as:Spec(G)={f(G,M)|M is a perfect matching of G}.In this paper,by applying the Ztransformation graph(resonance graph)we show that for any polyomino with perfect matchings and any even polygonal chain,their forcing spectra are integral intervals.Further we obtain some sharp bounds on maximum and minimum forcing numbers of hexagonal chains with given number of kinks.Forcing spectra of two extremal chains are determined.
