摘要：A signed graph is a simple graph where each edge receives a sign positive or negative. Such graphs are mainly used in social sciences where individuals represent vertices friendly relation between them as a positive edge and enmity as a negative edge. In signed graphs, we define these relationships (edges) as of friendship (“” edge) or hostility (“” edge). A 2-path product signed graph of a signed graph is defined as follows: the vertex set is the same as and two vertices are adjacent if and only if there exists a path of length two between them in . The sign of an edge is the product of marks of vertices in where the mark of vertex in is the product of signs of all edges incident to the vertex. In this paper, we give a characterization of 2-path product signed graphs. Also, some other properties such as sign-compatibility and canonically-sign-compatibility of 2-path product signed graphs are discussed along with isomorphism and switching equivalence of this signed graph with 2-path signed graph.
