Let n and k be integers with n> 2k n> 2 k, k ≥ 1 k≥ 1. We denote by H (n, k) the bipartite
Kneser graph, that is, a graph with the family of k-subsets and (nk nk)-subsets of n={1, 2 …

Abstract Let n> 3 n> 3 and 0< k< n 2 0< k< n 2 be integers. In this paper, we investigate
some algebraic properties of the line graph of the graph Q_n (k, k+ 1) Q n (k, k+ 1) where …

Let $ n $ and $ k $ be integers with $ n> k\geq1 $ and $[n]=\{1, 2,..., n\} $. The $
bipartite\Kneser\graph $$ H (n, k) $ is the graph with the all $ k $-element and all ($ nk $) …

Let $ G=(V, E) $ be a connected graph with the vertex-set $ V $ and the edge-set $ E $. The
subdivision graph $ S (G) $ of the graph $ G $ is obtained from $ G $ by adding a vertex in …

Let $\Omega $ be a $ m $-set, where $ m> 1$, is an integer. The Hamming graph $ H (n, m)
$, has $\Omega^{n} $ as its vertex-set, with two vertices are adjacent if and only if they differ …

Let $ k\geq 1$ be an integer and $ n= 3k-1$. Let $\mathbb {Z} _n $ denote the additive
group of integers modulo $ n $ and let $ C $ be the subset of $\mathbb {Z} _n $ consisting of …

Let $ G_n=\mathbb {Z} _n\times\mathbb {Z} _n $ for $ n\geq 4$ and $ S=\{(i, 0),(0, i),(i, i):
1\leq i\leq n-1\}\subset G_n $. Define $\Gamma (n) $ to be the Cayley graph of $ G_n $ with …

Let $\Gamma=(V, E) $ be a graph. The square graph $\Gamma^ 2$ of the graph $\Gamma $
is the graph with the vertex set $ V (\Gamma^ 2)= V $ in which two vertices are adjacent if …

Let $ G $ be a finite abelian group written additively with identity $0 $, and $\Omega $ be an
inverse closed generating subset of $ G $ such that $0\notin\Omega $. We say that $\Omega …

Let $ G_n=\mathbb {Z} _n\times\mathbb {Z} _n $ for $ n\geq 4$ and $ S=\{(i, 0),(0, i),(i, i):
1\leq i\leq n-1\}\subset G_n $. Define $\Gamma (n) $ to be the Cayley graph of $ G_n $ with …