A signed k-partite graph (signed multipartite graph) is a k-partite graph in which each edge is assigned a positive or a negative sign. If G(V1, V2, · · · , Vk) is a signed k-partite graph with Vi = {vi1, vi2, · · · , vini}, 1 ≤ i ≤ k, the signed degree of vij is sdeg(vij) = dij = d + ij − d − ij , where 1 ≤ i ≤ k, 1 ≤ j ≤ ni and d + ij(d − ij) is the number of positive (negative) edges inciden...

In a signed graph G, a negative clique is a complete subgraph having negative edges only. In this article, we give characteristic polynomial expressions, and eigenvalues of some signed graphs having negative cliques. This includes signed cycle graph, signed path graph, a complete graph with disjoint negative cliques, and star block graph with negative cliques.

A graph whose edges are labeled either as positive or negative is called a signed graph. A signed graph is said to be net-regular if every vertex has constant net-degree k, namely, the difference between the number of positive and negative edges incident with a vertex. In this paper, we analyze some properties of co-regular signed graphs which are net-regular signed graphs with the underlying g...

The nullity of a graph is the multiplicity of the eigenvalues zero in its spectrum. A signed graph is a graph with a sign attached to each of its edges. In this paper, we obtain the coefficient theorem of the characteristic polynomial of a signed graph, give two formulae on the nullity of signed graphs with cut-points. As applications of the above results, we investigate the nullity of the bicy...

A signed graph [G,Σ] is a graph G together with an assignment of signs + and − to all the edges of G where Σ is the set of negative edges. Furthermore [G,Σ1] and [G,Σ2] are considered to be equivalent if the symmetric difference of Σ1 and Σ2 is an edge cut of G. Naturally arising from matroid theory, several notions of graph theory, such as the theory of minors and the theory of nowhere-zero fl...

If G = (V, E, σ) is a finite signed graph, a function f : V → {−1, 0, 1} is a minusdominating function (MDF) of G if f(u) +summation over all vertices v∈N(u) of σ(uv)f(v) ≥ 1 for all u ∈ V . In this paper we characterize signed paths and cycles admitting an MDF.