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 functionσ:E→{+1,−1}assigning a positive or negative sign to each edge.In this paper,we present a more elementary...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 functionσ: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.展开更多
文摘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 functionσ: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.
