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 …

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 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 …

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 …

For any given $ n, m\in\mathbb {N} $ with $ m< n $, the Johnson graph $ J (n, m) $ is defined
as the graph whose vertex set is $ V=\{v\mid v\subseteq [n]=\{1,..., n\},| v|= m\} $, where two …

Let B (n, k) be the subgraph of the Boolean lattice BL n induced by the k th and (k+ 1) th
layers. The distance spectrum of BL n was obtained by Aalipour et al. and Koolen et al …

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 $\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 …