##### DIVISOR TOPOLOGIES AND THEIR ENUMERATION

F. Esmaeeli; K. Mirzavaziri; M. Mirzavaziri

Volume 10, Issue 1 , September 2022, , Pages 111-119
##### Abstract
‎For a positive integer $m$‎, ‎a subset of divisors of $m$ is called a \textit{divisor topology on $m$} if it contains $1$ and $m$ and it is closed under taking $\gcd$ and $\rm lcm$‎. ‎If $m=p_1\dots p_n$ is a square free positive integer‎, ‎then a divisor topology $m$ corresponds ...  Read More

##### THE (△,□)-EDGE GRAPH G△,□ OF A GRAPH G

Gh. A. Nasiriboroujeni; M. Mirzavaziri; A. Erfanian

Volume 8, Issue 1 , September 2020, , Pages 83-93
##### Abstract
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 ...  Read More