Sign-Compatibility of Some Derived Signed Graphs
DOI:
https://doi.org/10.12723/mjs.23.1Keywords:
Sign-compatible, ×-line sigraph, semi-total line sigraph, semi- total point sigraph, total sigraph.Abstract
A signed graph (or sigraph in short) is an ordered pair S = (Su, σ), where Su is a graph G = (V, E), called the underlying graph of S and σ : E → {+1, −1} is a function from the edge set E of Su into the set {+1, −1}, called the signature of S. A sigraph S is sign-compatible if there exists a marking µ of its vertices such that the end vertices of every negative edge receive ‘−1’ marks in µ and no positive edge does so. In this paper, we characterize S such that its ×-line sigraphs, semi-total line sigraphs, semi-total point sigraphs and total sigraphs are sign-compatible.
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