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 …

For a simple graph F, let Ex (n, F) and E x sp (n, F) denote the set of graphs with the
maximum number of edges and the set of graphs with the maximum spectral radius in an n …

Abstract The (k, r)-fan is the graph consisting of k copies of the complete graph K r which
intersect in a single vertex, and is denoted by F k, r. Erdős et al.(1995)[14] determined the …

Let F k be the (friendship) graph obtained from k triangles by sharing a common vertex. The
F k-free graphs of order n which attain the maximal spectral radius was firstly characterized …

The $ kK_ {r+ 1} $ is the union of $ k $ disjoint copies of $(r+ 1) $-clique. Moon [Canad. J.
Math. 20 (1968) 95--102] and Simonovits [Theory of Graphs (Proc. colloq., Tihany, 1996)] …

Given a graph family $\mathcal {H} $ with $\min_ {H\in\mathcal {H}}\chi (H)= r+ 1\geq 3$. Let
${\rm ex}(n,\mathcal {H}) $ and ${\rm spex}(n,\mathcal {H}) $ be the maximum number of …

The generalized Tur\'an number $\mathrm {ex}(n, H, F) $ is the maximum number of copies
of $ H $ in $ n $-vertex $ F $-free graphs. We consider the case where $\chi (H)<\chi (F) …

For a graph H, the Turán number of H, denoted by ex (n, H), is the maximum number of
edges of an n‐vertex H‐free graph. Let g (n, H) denote the maximum number of edges not …

Given a graph H and an integer p, the edge blow-up H p+ 1 of H is the graph obtained from
replacing each edge in H by a clique of order p+ 1 where the new vertices of the cliques are …

The planar Turán number of a given graph H, denoted by ex P (n, H), is the maximum
number of edges over all planar graphs on n vertices that do not contain a copy of H as a …