ABSTRACT
Common-Edge signed graph C E ( S ) of a signed graph S is a signed graph whose vertex-set is the pairs of adjacent edges in S and two vertices are adjacent if the corresponding pairs of adjacent edges of S have exactly one edge in common, with the sign same as that of Common-Edge. S -Marked signed graph T is a signed graph which receives the marking µ due to the signed graph S called marker. Further, T is S -consistent if a marker S is defined and if S -marking µ of T with respect to which marked signed graph T µ is consistent. In this paper, we give an algorithm to detect if C E ( S ) is S -consistent or not and determine its complexity. ⢠Algorithm to detect if C E ( S ) is S -consistent or not. ⢠Determination of algorithm's complexity.
