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On •-Line Signed Graphs L•(S)

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Sinha D., Dhama A.

Discussiones Mathematicae Graph Theory

2015

tom 35

nr 2

215-227

A signed graph (or sigraph for 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 → {+,−} is a function from the edge set E of Su into the set {+,−}. For a sigraph S its •-line sigraph, L•(S) is the sigraph in which the edges of S are represented as vertices, two of these vertices are defined adjacent whenever the corresponding edges in S have a vertex in common, any such L-edge ee′ has the sign given by the product of the signs of the edges incident with the vertex in e ∩ e′. In this paper we establish a structural characterization of •-line sigraphs, extending a well known characterization of line graphs due to Harary. Further we study several standard properties of •-line sigraphs, such as the balanced •-line sigraphs, sign-compatible •-line sigraphs and C-sign-compatible •-line sigraphs.

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1 Discussiones Mathematicae Graph Theory

1 Dhama A.

1 Sinha D.

1 2015

Wyniki wyszukiwania

On •-Line Signed Graphs L•(S)