Algorithmic approach to find [Formula: see text]-consistency in Common-Edge signed graph

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