TY - JOUR

T1 - On the independence polynomial of the corona of graphs

AU - Levit, Vadim E.

AU - Mandrescu, Eugen

N1 - Publisher Copyright:
© 2016 Elsevier B.V. All rights reserved.

PY - 2016/4/20

Y1 - 2016/4/20

N2 - Let α(G) be the cardinality of a largest independent set in graph G. If sk is the number of independent sets of size k in G, then I(G;x)=s0+s1x+⋯+sαxα, α=α(G), is the independence polynomial of G (Gutman and Harary, 1983). I(G;x) is palindromic if sα-i=si for each iε{0,1,⋯,⌊α/2⌋}. The corona of G and H is the graph G⊙H obtained by joining each vertex of G to all the vertices of a copy of H (Frucht and Harary, 1970). In this paper, we show that I(G⊙H;x) is palindromic for every graph G if and only if H=Kr-e,r≥2. In addition, we connect realrootness of I(G⊙H;x) with the same property of both I(G;x) and I(H;x).

AB - Let α(G) be the cardinality of a largest independent set in graph G. If sk is the number of independent sets of size k in G, then I(G;x)=s0+s1x+⋯+sαxα, α=α(G), is the independence polynomial of G (Gutman and Harary, 1983). I(G;x) is palindromic if sα-i=si for each iε{0,1,⋯,⌊α/2⌋}. The corona of G and H is the graph G⊙H obtained by joining each vertex of G to all the vertices of a copy of H (Frucht and Harary, 1970). In this paper, we show that I(G⊙H;x) is palindromic for every graph G if and only if H=Kr-e,r≥2. In addition, we connect realrootness of I(G⊙H;x) with the same property of both I(G;x) and I(H;x).

KW - Corona

KW - Independence polynomial

KW - Independent set

KW - Palindromic polynomial

KW - Perfect graph

KW - Real root

KW - Self-reciprocal sequence

UR - http://www.scopus.com/inward/record.url?scp=84949256647&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2015.09.021

DO - 10.1016/j.dam.2015.09.021

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AN - SCOPUS:84949256647

SN - 0166-218X

VL - 203

SP - 85

EP - 93

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -