Spectral radius and Hamiltonian graphs

Spectral Radius and Some Hamiltonian Properties of Graphs

On graphs whose spectral radius

The structure of graphs whose largest eigenvalue is bounded by 3 2 √ 2 (≈ 2.1312) is investigated. In particular, such a graph can have at most one circuit, and has a natural quipu structure.

Spectral radius of bipartite graphs

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.

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 ...