Shahrood University of TechnologyJournal of Algebraic Systems2345-51288120200901THE (△,□)-EDGE GRAPH G△,□ OF A GRAPH G8393176810.22044/jas.2019.8314.1411ENGh. A.NasiriboroujeniDepartment of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159,
Mashhad 91775, Iran.M.MirzavaziriDepartment of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159,
Mashhad 91775, Iran.A.ErfanianDepartment of Pure Mathematics and Center of Excellence in Analysis on Algebraic
Structures, Ferdowsi University of Mashhad, Mashhad, Iran.Journal Article20190506To 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 $G_{\triangle,\square}$.https://jas.shahroodut.ac.ir/article_1768_14cc474d2aefb94874aaa688ee9a3396.pdf