%0 Journal Article %T THE (△,□)-EDGE GRAPH G△,□ OF A GRAPH G %J Journal of Algebraic Systems %I Shahrood University of Technology %Z 2345-5128 %A Nasiriboroujeni, Gh. A. %A Mirzavaziri, M. %A Erfanian, A. %D 2020 %\ 09/01/2020 %V 8 %N 1 %P 83-93 %! THE (△,□)-EDGE GRAPH G△,□ OF A GRAPH G %K Graph Theory %K enumerative in graph theory %K enumerative in combinatorics %R 10.22044/jas.2019.8314.1411 %X 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 $G_{\triangle,\square}$. %U https://jas.shahroodut.ac.ir/article_1768_14cc474d2aefb94874aaa688ee9a3396.pdf