具有固定直径单圈图的Estrada指标
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摘要
针对具有固定直径的奇单圈图类中Estrada指标的最大图,通过不断缩小它所在的范围,证明了Δ_n~d是具有固定直径的奇单圈图类中Estrada指标最大的唯一图.其中,Δ_n~d表示在三角形的一个顶点粘上n-d-2条悬挂边和一条长为[d/2]的路,另一个顶点粘上一条长为[d/2]-1的路所得到的图.
In view of the unique graph with maximum Estrada index among the odd unicyclic graphs with fixed diameter,make the range of it narrow. In this paper we show that Δdnis the unique graph with maximum Estrada index among the odd unicyclic graphs with fixed diameter. Let Δdnbe the graph which is obtained from a triangle by attaching n-d-2 pendant edges and a path of length [d/2] at one vertex of it,and a path of length [d/2]-1 to another vertex,respectively.
In view of the unique graph with maximum Estrada index among the odd unicyclic graphs with fixed diameter,make the range of it narrow. In this paper we show that Δdnis the unique graph with maximum Estrada index among the odd unicyclic graphs with fixed diameter. Let Δdnbe the graph which is obtained from a triangle by attaching n-d-2 pendant edges and a path of length [d/2] at one vertex of it,and a path of length [d/2]-1 to another vertex,respectively.
引文
[1]BAMDAD H,ASHRAF F,GUTMAN I.Lower bounds for Estrada index and Laplacian Estrada index[J].Applied Mathematics Letters,2010,23(7):739-742.
[2]FATH-TABAR G H,ASHARFI A R.New upper bounds for Estrada index of bipartite graphs[J].Linear Algebra and Its Applications,2011,435(10):2607-2611.
[3]DU Z B,ZHOU B.The Estrada index of unicyclic graphs[J].Linear Algebra and its Applications,2012,436(9):3149-3159.
[4]WANG L,FAN Y Z,WANG Y.Maximum Estrada index of bicyclic graphs[J].Discrete Applied Mathematics,2015,180(10):194-199.
[5]滕海滨.单圈图的匹配与Estrada指标[D].合肥:安徽大学,2013:1-30.
[6]CVETKOVIC D M,DOOB M,SACHS H.Spectra of graphs theory and application[M].New York:Academic Press,1980.
[7]WANG W H,XU W W.Graphs with the maximal Estrada indices[J].Linear Algebra and its Applications,2014,446(1):314-328.
[2]FATH-TABAR G H,ASHARFI A R.New upper bounds for Estrada index of bipartite graphs[J].Linear Algebra and Its Applications,2011,435(10):2607-2611.
[3]DU Z B,ZHOU B.The Estrada index of unicyclic graphs[J].Linear Algebra and its Applications,2012,436(9):3149-3159.
[4]WANG L,FAN Y Z,WANG Y.Maximum Estrada index of bicyclic graphs[J].Discrete Applied Mathematics,2015,180(10):194-199.
[5]滕海滨.单圈图的匹配与Estrada指标[D].合肥:安徽大学,2013:1-30.
[6]CVETKOVIC D M,DOOB M,SACHS H.Spectra of graphs theory and application[M].New York:Academic Press,1980.
[7]WANG W H,XU W W.Graphs with the maximal Estrada indices[J].Linear Algebra and its Applications,2014,446(1):314-328.