A signed bipartite graph G(U, V) is a bipartite graph in which each edge is assigned a positive or a negative sign. The signed degree of a vertex x in G(U, V) is the number of positive edges incident with x less the number of negative edges incident with x. The set S of distinct signed degrees of the vertices of G(U, V) is called its signed degree set. In this paper, we prove that every set of ...

This paper is motivated by the concept of the signed k-domination problem and dedicated to the complexity of the problem on graphs. For any fixed nonnegative integer k, we show that the signed k-domination problem is NP-complete for doubly chordal graphs. For strongly chordal graphs and distance-hereditary graphs, we show that the signed k-domination problem can be solved in polynomial time. We...

A signed graph is a together with an assignment of signs to the edges. closed walk in said be positive (negative) if it has even (odd) number negative edges, counting repetition. Recognizing walks as one key structural properties graph, we define homomorphism (G,?) (H,?) mapping vertices and edges G (respectively) H which preserves incidence, adjacency walks. In this work first give characteriz...

In 1983, Bouchet proposed a conjecture that every flow-admissible signed graph admits nowhere-zero 6-flow. himself proved such graphs admit 216-flows and Zýka further 30-flows. this paper we show 11-flow.