Algorithmic approach to find -consistency in Common-Edge signed graph

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