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...
A signed graph (or sigraph in short) is an ordered pair , where is a graph G = (V,E), called the underlying graph of S and σ:E → +, - is a function from the edge set E of into the set +,-, called the signature of S. The ×-line sigraph of S denoted by is a sigraph defined on the line graph of the graph by assigning to each edge ef of , 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...
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