Unimodality of Independence Polynomials of the Cycle Cover Product of Graphs  

作　　者：Bao Xuan ZHU 

机构地区：[1]School of Mathematics and Statistics,Jiangsu Normal University,Xuzhou 221116,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第5期858-868,共11页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.11971206,12022105);Natural Science Foundation for Distinguished Young Scholars of Jiangsu Province(Grant No.BK20200048)。

摘　　要：An independent set in a graph G is a set of pairwise non-adjacent vertices.Let ik(G)denote the number of independent sets of cardinality k in G.Then its generating function I(G;x)=∑^(α(G))^(k=0)ik(G)x^(k),is called the independence polynomial of G(Gutman and Harary,1983).In this paper,we introduce a new graph operation called the cycle cover product and formulate its independence polynomial.We also give a criterion for formulating the independence polynomial of a graph.Based on the exact formulas,we prove some results on symmetry,unimodality,reality of zeros of independence polynomials of some graphs.As applications,we give some new constructions for graphs having symmetric and unimodal independence polynomials.

关 键 词：Independence polynomials UNIMODALITY LOG-CONCAVITY real zeros SYMMETRY cycle cover product of graphs 

分 类 号：O157.5[理学—数学]