For a simple connected graph Γ with node set V (Γ)={w1, w2,..., wn} and degree sequence
di, the atom-bond connectivity (ABC) matrix of Γ has an (ij)-th entry√ di+ dj− 2 didj if wi is …

For a simple connected graph G of order n, the normalized Laplacian is a square matrix of
order n, defined as ℒ (G)= D (G)−<? A3B2 [thinspace]?> 1 2 L (G) D (G)−<? A3B2 …

For a simple graph G, the generalized adjacency matrix A α (G) is defined as A α (G)= α D
(G)+(1− α) A (G), α∈[0, 1], where A (G) is the adjacency matrix and D (G) is the diagonal …

The work in this thesis concerns the investigation of eigenvalues of the Laplacian matrix,
normalized Laplacian matrix, signless Laplacian matrix and distance signless Laplacian …

For a finite group 𝒢, the power graph 𝒫 (𝒢) is a connected simple graph, whose vertex set is
the set of elements of 𝒢 and two vertices are connected by an edge if and only if one is the …

Let G be a finite group with the identity element e. The proper order graph of G, denoted by
S∗(G), is an undirected graph with a vertex set G\{e}, where two distinct vertices x and y are …

Given a finite group G, the coprime graph of G, denoted by r (G), is defined as an undirected
graph with the vertex set G, and for distinct x, y∈ G, x is adjacent to y if and only if (o (x), o …

For a square matrix M of order n partitioned into m 2 blocks B ij, the quotient matrix Q is a
square matrix of order k (m≤ k≤ n-1) with (i, j)-th entries as the average of the row …

Let G be a finite group with the identity element e. The proper order graph of G, denoted by
ℒ*(G), is an undirected graph with a vertex set G\{e}, where two distinct vertices x and y are …

Given a finite group G, the coprime graph of G, denoted by Γ (G), is defined as an undirected
graph with the vertex set G, and for distinct x, y∈ G, x is adjacent to y if and only if (o (x), o …