Non-inverse signed graph of a group - Amreen, J.; Naduvath, S. (Carpathian Mathematical Publications, 2024)
Let G be a group with binary operation *. The non-inverse graph (in short, i^*-graph) of G, denoted by Γ, is a simple graph with vertex set consisting of elements of G and two vertices x, y Γ are adjacent if x and y are not inverses of each other. That is, x- y if and only if x* y eq i_G eq y * x, where i_G is the identity element of G. In this paper, we extend the study of i^*-graphs to signed graphs by defining i^*-signed graphs. We characterize the graphs for which the i^*-signed graphs and negated i^*-signed graphs are balanced, sign-compatible, consistent and k-clusterable. We also obtain the frustration index of the i^*-signed graph. Further, we characterize the homogeneous non-inverse signed graphs and study the properties like net-regularity and switching equivalence.