图的邻接矩阵的行列式与积和式的递推表达式  

The Recurrence Expressions of Determinant and Permanent of Adjacency Matrix of Graph

作　　者：扈生彪[1] 

机构地区：[1]青海民族大学数学学院,青海西宁810007

出　　处：《数学的实践与认识》2011年第15期222-227,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10861009)

摘　　要：设A(G)是简单图G的邻接矩阵,H是由G的独立边和不交圈组成的生成子图的集合,e是H中某个图的独立边,C是H中图的圈,且e∈E(C).记G-e是G的删边子图,G\W是从G中删去导出子图W中的顶点及其关联边后得到的图.那么A(G)的行列式为detA(G)=detA(G-e)-detA(G\e)-2(-1)^(|V(C)|)detA(G\C)A(G)的积和式为perA(G)=perA(G-e)+perA(G\e)+2perA(G\C)这里,C取遍H中图的经过边e的圈.Let A（G） be an adjacency matrix of simple undirected graph G, H is a set of spanning subgraph of G consisting of disjoint edges and cycles, e is a disjoint edge of some graph in H , C is cycle of graph in H ,and e ∈ E（C）. G - e is the subgraph of G obtained by deleting the edge e, G ／ W is the subgraph of G obtained by deleting the vertices in W and all edges incident with them. Then the determinant of A（G） is detA（G）=detA（G-e）-detA（G／e）-2∑ c（-1）^｜V（C）｜detA（G／C） A（G） Thepermanent of A（G） is perA（G）=perA（G-e）＋perA（G／e）＋2∑ cperA（G／C） Where,C ranges over the cycles of pass through the edge e of graphs in H.

关 键 词：行列式 积和式 邻接矩阵 生成子图 

分 类 号：O157.5[理学—数学]