玫瑰图的Hosoya指标与永久和
On the Hosoya Index and Permanental Sum of Rose Graphs
DOI:10.12677/PM.2024.148302,PDF,下载: 2浏览: 40
作者:苏 坤,王佳亿*：青海民族大学数学与统计学院，青海 西宁
关键词:玫瑰图；永久和；Hosoya指标；Rose Graphs；Permanental Sum；Hosoya Index
摘要:假设图 G 是一个简单无向图,则图 G的 Hosoya 指标指的是该图的所有匹配数目之和.令I是单位矩阵,A(G) 是图 G 的邻接矩阵,则积和多项式定义为 π(G,x)= per(xI-A(G)).图 G 的永久和定义为其积和多项式系数的绝对值之和.本文研究了三圈图中玫瑰图的 Hosoya 的第二小并刻画了极图:其次,研究了玫瑰图永久和的第二小并刻画了极图。
Abstract:Let G be a simple and undirected graph. The Hosoya index Z(G) of G is defined to be the total number of matchings of G. Let I be an identity matrix and A(G) be an adjacency matrix of G. Then the permanental polynomial of G is defined as π(G,x) = per(xI-A(G)). The permanental sum of G is defined as the sum of the absolute values of all coefficients of π(G,x). In this paper, we prove the second smallest Hosoya index of rose graphs and determine the extremal graphs. Besides, we prove the second smallest permanental sum of rose graphs and determine the extremal graphs.
文章引用：苏坤, 王佳亿. 玫瑰图的Hosoya指标与永久和[J]. 理论数学, 2024, 14(8): 46-53. https://doi.org/10.12677/PM.2024.148302

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