On degree product induced signed graphs of graphs

A signed graph is a graph with positive or negative signs assigned to edges. An induced signed graph is a signed graph constructed from a given graph according to some pre-defined protocols. An induced signed graph of a graph G is a signed graph in which each edge uv receives a sign (−1)|φ(v)−φ(u)|, where φ : V(G) → ℤ. In this paper, we discuss degree product induced signed graphs and determine the structural properties of these signed graphs such as balancing, clustering, regularity and co-regularity.