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Discussiones Mathematicae Graph Theory 31(4) (2011) 625-638
DOI: https://doi.org/10.7151/dmgt.1570

Some Results on Semi-Total Signed Graphs

Deepa Sinha and Pravin Garg Centre for Mathematical Sciences Banasthali University Banasthali--304022, Rajasthan, India

Abstract

A signed graph (or sigraph in short) is an ordered pair S = (S^u, σ), where S^u is a graph G = (V, E), called the underlying graph of S and σ:E → {+, −} is a function from the edge set E of S^u into the set {+, −}, called the signature of S. The ×-line sigraph of S denoted by L_×(S) is a sigraph defined on the line graph L(S^u) of the graph S^u by assigning to each edge ef of L(S^u), the product of signs of the adjacent edges e and f in S. In this paper, first we define semi-total line sigraph and semi-total point sigraph of a given sigraph and then characterize balance and consistency of semi-total line sigraph and semi-total point sigraph.

Keywords: sigraph, semi-total line sigraph, semi-total point sigraph, balanced sigraph, consistent sigraph

2010 Mathematics Subject Classification: Primary: 05C22;
Secondary: 05C75.

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Received 11 October 2009
Revised 30 September 2010
Accepted 1 October 2010