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 …

A k-tree is a spanning tree in which every vertex has degree at most k. In this paper, we
provide a sufficient condition for the existence of ak-tree in a connected graph with fixed …

The study of the existence of Hamiltonian cycles in a graph is a classical problem in graph
theory. By incorporating toughness and spectral conditions, we can consider Chvátal's …

The toughness t(G) of a connected graph G is defined as t(G)=\min{|S|c(GS)\}, in which the
minimum is taken over all proper subsets S⊂V(G) such that c(GS)>1, where c(GS) denotes …

The toughness t (G) of a graph G=(V, E) is defined as t (G)= min {| S| c (G− S)}, in which the
minimum is taken over all S⊂ V such that G− S is disconnected, where c (G− S) denotes the …

Let α′ and μ i denote the matching number of a non-empty simple graph G with n vertices
and the i th smallest eigenvalue of its Laplacian matrix, respectively. In this paper, we prove …

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Given a connected graph G, the toughness τ G is defined as the minimum value of the ratio|
S|/ω G− S, where S ranges over all vertex cut sets of G, and ω G− S is the number of …

A d-regular graph on n vertices with the second largest absolute eigenvalue at most λ is
called an (n, d, λ)-graph. The celebrated expander mixing lemma for (n, d, λ)-graphs builds a …

Full article: Spectral conditions for graphs to be β-deficient involving minimum degree Skip to
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