The commuting graph of a finite non-abelian group G with center Z (G), denoted by Γ c (G), is
a simple undirected graph whose vertex set is G∖ Z (G), and two distinct vertices x and y are …

Let G be a simple graph of order n. The eigenvalue of a graph G is the eigenvalue of its
adjacency matrix. The energy E (G) of G is the sum of absolute values of its eigenvalues. A …

Let G be a graph on n vertices with vertex set V\(G\) and let S⊆ V\(G\) with\| S\|= α. Denote
by GS, the graph obtained from G by adding a self-loop at each of the vertices in S. In this …

Let G be a simple graph on n vertices with vertex set V (G). The energy of G, denoted by,
$\mathcal {E}(G) $ is the sum of all absolute values of the eigenvalues of the adjacency …

The energy E (G) of a graph G is defined as the sum of the absolute values of the
eigenvalues of its adjacency matrix. If the energy of a graph G of order n is equal to its order …