Let G be a finite non-abelian group and Γ nc (G) be its non-commuting graph. In this paper,
we compute spectrum and energy of Γ nc (G) for certain classes of finite groups. As a …

In this paper, we compute the Laplacian spectrum of non-commuting graphs of some
classes of finite non-abelian groups. Our computations reveal that the non-commuting …

Let $ G $ be a finite non-solvable group with solvable radical $ Sol (G) $. The solvable graph
$\Gamma_s (G) $ of $ G $ is a graph with vertex set $ G\setminus Sol (G) $ and two distinct …

arXiv:1705.10611v1 [math.GR] 27 May 2017 Page 1 arXiv:1705.10611v1 [math.GR] 27 May
2017 On Laplacian energy of non-commuting graphs of finite groups Parama Dutta and …

Let G be a non-abelian group. The non-commuting graph of group G, shown by ГG, is a
graph with the vertex set G\Z (G), where Z (G) is the center of group G. Also two distinct …

The non-commuting graph of a non-abelian group $ G $ with center $ Z (G) $ is a simple
undirected graph whose vertex set is $ G\setminus Z (G) $ and two vertices $ x, y $ are …

Let G be a group, and Sol (G)={x∈ G:⟨ x, y⟩ is solvable for all y∈ G}. We associate a graph
NS G (called the non-solvable graph of G) with G whose vertex set is G\Sol (G) and two …

Let R be a finite ring and r∈ R. The r-noncommuting graph of R, denoted by Γ R r, is a
simple undirected graph whose vertex set is R and two vertices x and y are adjacent if and …

Let H be a subgroup of a finite non-abelian group G and g∈ G. Let Z (H, G)={x∈ H: xy=
yx,∀ y∈ G}. We introduce the graph Δ H, G g whose vertex set is G\Z (H, G) and two distinct …

Let Z (G) be the center of a finite non-abelian group G. The non-commuting graph of G is a
simple undirected graph with vertex set G∖ Z (G), and two vertices u and v are adjacent if …