Spectral radius and Hamiltonicity of graphs

Spectral radius and Hamiltonicity of graphs with large minimum degree

We extend some recent results on sufficient conditions for Hamiltonian paths and cycles in G. Let G be a graph of order n and λ (G) be the spectral radius of its adjacency matrix. One of the main results of the paper is the following theorem: Let k 2, n k3 + k + 4, and let G be a graph of order n, with minimum degree δ (G) k. If λ (G) n k 1, then G has a Hamiltonian cycle, unless G = K1 _ (Kn k...

Signless Laplacian spectral radius and Hamiltonicity of graphs with large minimum degree

In this paper, we establish a tight sufficient condition for the Hamiltonicity of graphs with large minimum degree in terms of the signless Laplacian spectral radius and characterize all extremal graphs. Moreover, we prove a similar result for balanced bipartite graphs. Additionally, we construct infinitely many graphs to show that results proved in this paper give new strength for one to deter...

Spectral radius of bipartite graphs

On Complementary Distance Signless Laplacian Spectral Radius and Energy of Graphs

Let $D$ be a diameter and $d_G(v_i, v_j)$ be the distance between the vertices $v_i$ and $v_j$ of a connected graph $G$. The complementary distance signless Laplacian matrix of a graph $G$ is $CDL^+(G)=[c_{ij}]$ in which $c_{ij}=1+D-d_G(v_i, v_j)$ if $ineq j$ and $c_{ii}=sum_{j=1}^{n}(1+D-d_G(v_i, v_j))$. The complementary transmission $CT_G(v)$ of a vertex $v$ is defined as $CT_G(v)=sum_{u in ...

Walks and the spectral radius of graphs

Given a graph G, write μ (G) for the largest eigenvalue of its adjacency matrix, ω (G) for its clique number, and wk (G) for the number of its k-walks. We prove that the inequalities wq+r (G) wq (G) ≤ μ (G) ≤ ω (G) − 1 ω (G) wr (G) hold for all r > 0 and odd q > 0. We also generalize a number of other bounds on μ (G) and characterize pseudo-regular and pseudo-semiregular graphs in spectral terms.