Document Type: Review Paper


1 Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran.

2 Department of Pure Mathematics and Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, Mashhad, Iran.


To a simple graph $G=(V,E)$, we correspond a simple graph $G_{\triangle,\square}$ whose vertex set is $\{\{x,y\}: x,y\in V\}$ and two vertices $\{x,y\},\{z,w\}\in G_{\triangle,\square}$ are adjacent if and only if $\{x,z\},\{x,w\},\{y,z\},\{y,w\}\in V\cup E$. The graph $G_{\triangle,\square}$ is called the $(\triangle,\square)$-edge graph of the graph $G$. In this paper, our ultimate goal is to provide a link between the connectedness of $G$ and $G_{\triangle,\square}$.