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 …

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 $ 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 …

The distance eigenvalues of a connected graph G are the eigenvalues of its distance matrix
D (G). A graph is called distance integral if all of its distance eigenvalues are integers. Let …

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 …

Abstract Given $ n, m\in\mathbb {N} $ with $ m< n $ and Let $ I=\{1,..., n\} $. The Johnson
graph $ J (n, m) $ is defined as the graph whose vertex set is $ V=\{v\mid v\subseteq I,| v …

This paper discusses the automorphism group of a class of weakly semiregular bipartite
graphs and its subclass called WSBEND graphs. It also tries to analyse the automorphism …

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 …

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 …