The generalized characteristic polynomial of the subdivision-vertex and subdivision-edge coronae

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	The generalized characteristic polynomial of the subdivision-vertex and subdivision-edge coronae
	Lu, Pengli; Miao, Yufang
刊名	ARS COMBINATORIA
	2016-10
卷号	129 页码:341-356
关键词	Spectrum Cospectral graphs Integral graphs Spanning trees Kirchhoff index Subdivision-vertex corona Subdivision edge corona
ISSN号	0381-7032
英文摘要	The subdivision graph S(G) of a graph G is the graph obtained by inserting a new vertex into every edge of G. Let G(1) and G(2) be two vertex disjoint graphs. The subdivision-vertex corona of G(1) and G(2), denoted by G(1) circle dot G(2), is the graph obtained from S(G(1)) and vertical bar V(G(1))vertical bar copies of G(2), all vertex-disjoint, by joining the ith vertex of V(G(1)) to every vertex in the ith copy of G(2). The subdivision-edge corona of G(1) and G(2), denoted by G(1) circle minus G(2), is the graph obtained from S(G(1)) and vertical bar I(G(1))vertical bar copies of G(2), all vertex-disjoint, by joining the ith vertex of I(G(1)) to every vertex in the ith copy of G(2), where I(G(1)) is the set of inserted vertices of S(G(1)). In this paper we determine the generalized characteristic polynomial of G(1) circle dot G(2) (respectively, G(1) circle dot G(2)). As applications, the results on the spectra of G(1) circle dot G(2) (respectively, G(1) circle minus G(2)) enable us to construct infinitely many pairs of Phi-cospectral graphs. The adjacency spectra of G(1) circle dot G(2) (respectively, G(1) circle minus G(2)) help us to construct many infinite families of integral graphs. By using the Laplacian spectra, we also obtain the number of spanning trees and Kirchhoff index of G(1) circle dot G(2) and G(1) circle minus G(2), respectively.
资助项目	Natural Science Foundation of China[11361033] ; Natural Science Foundation of Gansu Province[1212RJZA029]
WOS研究方向	Mathematics
语种	英语
出版者	CHARLES BABBAGE RES CTR
WOS记录号	WOS:000384963500027
状态	已发表
内容类型	期刊论文
源URL	[http://119.78.100.223/handle/2XXMBERH/33574]
专题	兰州理工大学
通讯作者	Lu, Pengli
作者单位	Lanzhou Univ Technol, Sch Comp & Commun, Lanzhou 730050, Gansu, Peoples R China
推荐引用方式 GB/T 7714	Lu, Pengli,Miao, Yufang. The generalized characteristic polynomial of the subdivision-vertex and subdivision-edge coronae[J]. ARS COMBINATORIA,2016,129:341-356.
APA	Lu, Pengli,&Miao, Yufang.(2016).The generalized characteristic polynomial of the subdivision-vertex and subdivision-edge coronae.ARS COMBINATORIA,129,341-356.
MLA	Lu, Pengli,et al."The generalized characteristic polynomial of the subdivision-vertex and subdivision-edge coronae".ARS COMBINATORIA 129(2016):341-356.