Nikiforov (2002) showed that if G is K r+ 1-free then the spectral radius ρ (G)≤ 2 m (1− 1∕
r), which implies that G contains C 3 if ρ (G)> m. In this paper, we follow this direction in …

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 …

A graph is color‐critical if it contains an edge whose removal reduces its chromatic number.
Let T n, k T_n,k be the Turán graph with nn vertices and kk parts. Given a graph HH, let ex …

A classic result in extremal graph theory, known as Mantel's theorem, implies that every non-
bipartite graph of order n with size m>⌊ n 2/4⌋ contains a triangle. Recently, by majority …

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 …

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 …