Characterization of 2-Path Product Signed Graphs with Its Properties

Algorithm 2

To check if the given signed graph is a 2-path product of some other signed graph.

Input. The adjacency matrix of signed graph and dimension

Output. If is a 2-path for some signed graph then returns its adjacency matrix .

Process

(1) We use Algorithm 1 to detect if is a 2-path signed graph.

(2) Use algorithm in [34] to check if is balanced.

(3) for to do

(4)   ; for to do

(5)     if then

(6)       ;

(7) ;

(8) for to do

(9)   

(10) if then

(11)   The given signed graph is not a 2-path product signed graph

(12) else

(13)   The given signed graph is a 2-path product signed graph