The total graph of a graph G, denoted by T (G), is defined to be the graph whose vertices are
the vertices and edges of G, with two vertices of T (G) adjacent if and only if the …

Let $ G $ be a graph with adjacency matrix $ A $. The transition matrix of $ G $ relative to $ A
$ is defined by $ H (t):=\exp {\left (-itA\right)},\; t\in\Rl $. The graph $ G $ is said to admit pretty …

A blow-up of n copies of a graph G is the graph obtained by replacing every vertex of G by
an independent set of size n, where the copies of two vertices in G are adjacent in the blow …

Twin vertices in simple unweighted graphs are vertices that have the same neighbours, and,
in the case of weighted graphs with possible loops, the corresponding incident edges have …

Let G be a graph with adjacency matrix AG. The transition matrix of G corresponding to AG is
denoted as HAG (t):= exp⁡(− it AG)(t∈ R, i=− 1). If there is some time τ∈ R such that HAG …

In this paper, we investigate the existence of Laplacian perfect state transfer and Laplacian
pretty good state transfer in edge complemented coronas. We give sufficient conditions for …

The transition matrix of a graph G corresponding to the adjacency matrix A is defined by H
(t)≔ exp− it A, where t∈ R. The graph is said to exhibit pretty good state transfer between a …

In this paper, we investigate the existence of fractional revival on Cayley graphs over finite
abelian groups. We give a necessary and sufficient condition for Cayley graphs over finite …

Strong cospectrality is an equivalence relation on the set of vertices of a graph that is of
importance in the study of quantum state transfer in graphs. We construct families of abelian …

We study the existence of quantum state transfer on non-integral circulant graphs. We find
that continuous-time quantum walks on quantum networks based on certain circulant graphs …