首页|Yet More Elementary Proof of Matrix-Tree Theorem for Signed Graphs
Yet More Elementary Proof of Matrix-Tree Theorem for Signed Graphs
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A signed graph G=(G,σ)is a graph G=(V(G),E(G))with vertex set V(G)and edge set E(G),together with a function σ:E → {+1,-1} assigning a positive or negative sign to each edge.In this paper,we present a more elementary proof for the matrix-tree theorem of signed graphs,which is based on the relations between the incidence matrices and the Laplcians of signed graphs.As an application,we also obtain the results of Monfared and Mallik about the matrix-tree theorem of graphs for signless Laplacians.
signed graphmatrix-tree theoremLaplaciansignless Laplacianincidence matrix
Shu Li、Jianfeng Wang
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School of Mathematics and Statistics,Shandong University of Technology Zibo,Shandong 255049,China
authors are supported by National Natural Science Foundation of China
NETL
NSTL
万方数据
维普
