Abstract Let G=(V, E) G=(V, E) be a graph with the vertex-set V and the edge-set E. Let N (v)
denote the set of neighbors of the vertex v of G. The graph G is called irreducible whenever …

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 …

The token graphs of graphs have been studied at least from the 80's with different names
and by different authors. The Johnson graph J (n, k) is isomorphic to the k-token graph of the …

A design graph is a regular bipartite graph in which any two distinct vertices of the same part
have the same number of common neighbors. This class of graphs has a close relationship …

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 …

The folded hypercube $ FQ_n $ is the Cayley graph Cay $(\mathbb {Z} _2^ n, S) $, where $
S=\{e_1, e_2,\dots, e_n\}\cup\{u= e_1+ e_2+\dots+ e_n\} $, and $ e_i=(0,\dots, 0, 1, 0 …

The folded hypercube $ FQ_n $ is the Cayley graph $ Cay (\mathbb {Z} _2^ n, S) $, where $
S=\{e_1, e_2,\dots, e_n\}\cup\{u= e_1+ e_2+\dots+ e_n\} $, $ e_i=(0,\dots, 0, 1, 0,\dots, 0) …