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

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 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...

The Randić index and signless Laplacian spectral radius of graphs

Given a connected graph G, the Randić index R(G) is the sum of 1 √ d(u)d(v) over all edges {u, v} of G, where d(u) and d(v) are the degree of vertices u and v respectively. Let q(G) be the largest eigenvalue of the singless Laplacian matrix of G and n = |V (G)|. Hansen and Lucas (2010) made the following conjecture:

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 ...

The signless Laplacian spectral radius of graphs with given degree sequences