Signed Degree Sequences in Signed Bipartite Graphs
نویسندگان
چکیده
A signed bipartite graph is a bipartite graph in which each edge is assigned a positive or a negative sign. Let G(U, V ) be a signed bipartite graph with U = {u1, u2, · · · , up} and V = {v1, v2, · · · , vq} . Then signed degree of ui is sdeg(ui) = di = d + i − d − i , where 1 ≤ i ≤ p and d+i ( d − i ) is the number of positive(negative) edges incident with ui , and signed degree of vj is sdeg(vj) = ej = e + j − e − j , where 1 ≤ j ≤ q and e + j ( e − j ) is the number of positive(negative) edges incident with vj . Clearly, |di| ≤ q and |ej | ≤ p . So the sequences α = [d1, d2, · · · , dp] and β = [e1, e2, · · · , eq] are called the signed degree sequences of G(U, V ) . In this paper, we give characterizations of signed degree sequences in signed bipartite graphs.
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