中山大学学报自然科学版 ›› 2019, Vol. 58 ›› Issue (6): 128-134.doi: 10.13471/j.cnki.acta.snus.2019.06.016

• 论文 • 上一篇    下一篇

单圈图永久和的极值

陈兰,吴廷增   

  1. 青海民族大学数学与统计学院,青海 西宁 810007
  • 收稿日期:2019-04-30 出版日期:2019-11-25 发布日期:2019-11-25

Extremal unicyclic graphs with respect to permanental sum

CHEN Lan, WU Tingzeng     

  1. School of Mathmatics and Statistics, Qinghai Nationalities University, Xining 810007,China
  • Received:2019-04-30 Online:2019-11-25 Published:2019-11-25

摘要:

G表示n个顶点的图。A(G)表示图G的邻接矩阵。图G的积和多项式为π(G,x)=per(xI-A(G)),其中I为n阶单位矩阵。图G的永久和是指积和多项式π(G,x)的系数的绝对值之和。刻画了n个顶点的单圈图中具有第三小至第七小永久和的极图。

关键词: 积和多项式, 单圈图, 永久和

Abstract:

Let G be a graph with n vertex, and A(G) be an adjacency matrix of a graph G. Then the polynomial π(G,x)=per(xI-A(G))  is called the permanental polynomial of G, where I the unit matrix of order n. The permanental sum of G is the sum of the absolute valutes of the cofficients of π(G,x). The unicyclic graphs having I th minimal permanental sum are determined, where, I=3,4,5,6,7.

Key words: unicyclic graph, permanental polynomial, permanental sum

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