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 …

Abstract A graph XX is said to be unstable if the direct product X× K 2 X*K_2 (also called the
canonical double cover of XX) has automorphisms that do not come from automorphisms of …

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 …

Consider G to be a simple graph with n vertices and m edges, and L (G) to be a Laplacian
matrix with Laplacian eigenvalues of μ 1, μ 2,…, μ n= zero. Write S k (G)=∑ i= 1 k μ i as 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 …

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 its‌‌distance eigenvalues are …

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 …