This survey is two-fold. We first report new progress on the spectral extremal results on the
Tur\'{a} n type problems in graph theory. More precisely, we shall summarize the spectral …

It is well known that spectral Turán type problem is one of the most classical problems in
graph theory. In this paper, we consider the spectral Turán type problem. Let G be a graph …

Let S n, 2 be the graph obtained by joining each vertex of K 2 to n− 2 isolated vertices, and
let S n, 2− be the graph obtained from S n, 2 by deleting an edge incident to a vertex of …

A well-known result of Nosal states that a graph G with m edges and λ (G)> m contains a
triangle. Nikiforov [Combin. Probab. Comput. 11 (2002)] extended this result to cliques by …

It is well-known that eigenvalues of graphs can be used to describe structural properties and
parameters of graphs. A theorem of Nosal states that if $ G $ is a triangle-free graph with $ m …

A well-known result in extremal spectral graph theory, known as Nosal's theorem, states that
if is a triangle-free graph on vertices, then, equality holds if and only if. Nikiforov [Linear …

The gem is the 5-vertex graph consisting of a 4-vertex path plus a vertex adjacent to each
vertex of the path. A graph is said to be gem-free if it does not contain gem as a subgraph. In …

It is well-known that Brualdi-Hoffman-Tur\'an-type problem asks what is the maximum
spectral radius $\lambda (G) $ of an $ F $-free graph $ G $ with $ m $ edges? It can be …

Abstract In 2017, Nikiforov [12] proposed the A α-matrix of a graph G, which is defined as the
convex linear combination of the adjacency matrix A (G) and the diagonal matrix of degrees …

Spectral graph theory is a captivating area of graph theory that employs the eigenvalues and
eigenvectors of matrices associated with graphs to study them. In this paper, we present a …