Gh. A. Nasiriboroujeni - Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box ۱۱۵۹, Mashhad ۹۱۷۷۵, Iran.
M. Mirzavaziri - Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box ۱۱۵۹, Mashhad ۹۱۷۷۵, Iran.
A. Erfanian - 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 ${{x,y}: x,yin V}$ and two vertices ${x,y},{z,w}in G_{triangle,square}$ are adjacent if and only if ${x,z},{x,w},{y,z},{y,w}in Vcup E$. 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 $G_{triangle,square}$.

Graph Theory, enumerative in graph theory, enumerative in combinatorics