Sinha Deepa, Sharma Deepakshi
Department of Mathematics, South Asian University, Akbar Bhawan Chanakyapuri, New Delhi 110021, India.
Comput Intell Neurosci. 2017;2017:1235715. doi: 10.1155/2017/1235715. Epub 2017 Jul 6.
A 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 [Formula: see text] 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.
A是一个简单图，其中每条边都被赋予一个正号或负号。这样的图主要用于社会科学领域，其中个体代表顶点，它们之间的友好关系用正边表示，敌对关系用负边表示。在带符号图中，我们将这些关系（边）定义为友谊（“+”边）或敌意（“-”边）。带符号图 的[公式：见文本]定义如下：顶点集与 相同，当且仅当在 中它们之间存在长度为二的路径时，两个顶点相邻。边的符号是 中顶点标记的乘积，其中 中顶点 的标记是与该顶点相关联的所有边的符号的乘积。在本文中，我们给出了2-路径乘积带符号图的一个特征。此外，还讨论了2-路径乘积带符号图的一些其他性质，如符号兼容性和规范符号兼容性，以及该带符号图与2-路径带符号图的同构和切换等价性。
