Vol. 11 No. 4 (2012): Mapana Journal of Sciences
Research Articles

Sign-Compatibility of Some Derived Signed Graphs

  • Deepa Sinha,
  • Ayushi Dhama
Deepa Sinha
Department of Mathematics, South Asian University, Akbar Bhawan, Chanakyapuri, New Delhi-110 021, India;
Ayushi Dhama
Centre for Mathematical Sciences, Banasthali University, Banasthali-304022, Rajasthan, India;
DOI: https://doi.org/10.12723/mjs.23.1

Published 2012-07-02

Keywords

  • 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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