In this paper, we study the maximum adjacency spectral radii of graphs of large order that do
not contain an even cycle of given length. For $ n> k $, let $ S_ {n, k} $ be the join of a clique …

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 …

Minors play a key role in graph theory, and extremal problems on forbidding minors have
attracted appreciable amount of interest in the past decades. In this paper, we focus on …

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 …

Turán-type problem is one of central problems in extremal graph theory. Erdős et al.[J.
Combin. Theory Ser. B 64 (1995) 89-100] obtained the exact Turán number of the friendship …

In this paper, we study a Turán-like problem in the context of signed graphs. Suppose that G˙
is a connected unbalanced signed graph of order n with e (G˙) edges and e−(G˙) negative …

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 …

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 …

In this paper, we give spectral conditions to guarantee the existence of two edge disjoint
cycles and two cycles of the same length. These two results can be seen as spectral …