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Canonical Consistency of Semi-total Point Signed Graphs

Sinha, Deepa, Garg, Pravin
National Academy science letters 2015 v.38 no.6 pp. 497-500
computer graphics, equations, mathematical theory
A signed graph (or sigraph in short) is an ordered pair [Formula: see text], where [Formula: see text] is a graph [Formula: see text] and [Formula: see text] is a function from the edge set [Formula: see text] of [Formula: see text] into the set [Formula: see text]. The canonical marking on [Formula: see text] is defined as: for each vertex [Formula: see text], [Formula: see text] where [Formula: see text] is the set of edges [Formula: see text] incident at [Formula: see text] in [Formula: see text]. A vertex [Formula: see text] is called negative if the value of marking of [Formula: see text] is negative. Let [Formula: see text] is canonically marked, then a cycle [Formula: see text] in [Formula: see text] is said to be canonically consistent if it contains an even number of negative vertices. If every cycle in [Formula: see text] is canonically consistent, then [Formula: see text] is called canonically consistent. In this paper, we characterize canonically consistent semi-total point sigraphs.