The Common Neighborhood Graph and Its Energy

Author(s):

Anwar Alwardi , Branko Arsic , Ivan Gutman , Nandappa D. Soner

Message:
Abstract:
Let $G$ be a simple graph with vertex set ${v_1,v_2,ldots,v_n}$. The common neighborhood graph (congraph) of $G$, denoted by $con(G)$, is the graph with vertex set ${v_1,v_2,ldots,v_n}$, in which two vertices are adjacent if and only they have at least one common neighbor in the graph $G$. The basic properties of $con(G)$ and of its energy are established.
Keywords:

Common neighborhood graph , Congraph , Spectrum (of graph) , Energy (of graph)

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:7 Issue: 2, Nov 2012
Page:
1
https://www.magiran.com/p1043205