Hamiltonian Properties Of Graphs Research Articles

Largest and smallest eigenvalues of matrices and some Hamiltonian properties of graphs

Largest and smallest eigenvalues of matrices and some Hamiltonian properties of graphs

Largest and smallest eigenvalues of matrices and some Hamiltonian properties of graphs

Largest and smallest eigenvalues of matrices and some Hamiltonian properties of graphs

Reciprocal degree distance and Hamiltonian properties of graphs

For a connected graph G, the reciprocal degree distance (RDD) of the graph G is defined as; RDD(G)=∑u≠vdegG⁡(u)+degG⁡(v)dG(u,v), where degG⁡(u) is the degree of u in G and dG(u,v) is the distance between u and v in G. In this article, we give sufficient condition for a graph to be traceable, Hamiltonian, Hamiltonian-connected in terms of RDD(G).

The Largest Eigenvalue of the Signless Laplacian and Some Hamiltonian Properties of Graphs

The Largest Eigenvalue of the Signless Laplacian and Some Hamiltonian Properties of Graphs

The Clique Number and Some Hamiltonian Properties of Graphs

The Clique Number and Some Hamiltonian Properties of Graphs

Corrigendum to “Combinations of some spectral invariants and Hamiltonian properties of graphs, Contrib. Math. 1 (2020) 54–56”

Corrigendum to “Combinations of some spectral invariants and Hamiltonian properties of graphs, Contrib. Math. 1 (2020) 54–56”

Combinations of some spectral invariants and Hamiltonian properties of graphs

Combinations of some spectral invariants and Hamiltonian properties of graphs

Laplacian spread and some Hamiltonian properties of graphs

The Laplacian spread of a graph is the difference between the largest and second smallest Laplaicain eigenvalues of the graph. Using the Laplacian spread of a graph, we in this note present sufficient conditions for some Hamiltonian properties of the graph.

Spectral radius and Hamiltonian properties of graphs, II

In this paper, we first present spectral conditions for the existence of in graphs (2-connected graphs) of order n, which are motivated by a conjecture of Erds. We also prove spectral conditions for the existence of Hamilton cycles in balanced bipartite graphs. This result presents a spectral analog of Moon-Moser's theorem on Hamilton cycles in balanced bipartite graphs, and extends a previous theorem due to Li and the second author for n sufficiently large. We conclude this paper with two problems on tight spectral conditions for the existence of long cycles of given lengths.

Distance signless Laplacian spectral radius and Hamiltonian properties of graphs

In this paper, we establish a sufficient condition on distance signless Laplacian spectral radius for a bipartite graph to be Hamiltonian. We also give two sufficient conditions on distance signless Laplacian spectral radius for a graph to be Hamilton-connected and traceable from every vertex, respectively. Furthermore, we obtain a sufficient condition for a graph to be Hamiltonian in terms of the distance signless Laplacian spectral radius of the complement of a graph G.

Signless Laplacian Spectral Radius and Some Hamiltonian Properties of Graphs

Using upper bounds for the signless Laplacian spectral radius of graphs established by Yu et al. [9], Wang et al. [8], Liu et al. [7], and Li et al. [5], we in this note present sufficient conditions which are based on the signless Laplacian spectral radius for some Hamiltonian properties of graphs.

Harary index and some Hamiltonian properties of graphs

For a nontrivial connected graph G, its Harary index H(G) is defined as ∑{u,v}⊆V(G)1dG(u,v), where dG(u,v) is the distance between vertices u and v. Hua and Wang (2013), using Harary index, obtained a sufficient condition for the traceable graphs. In this note, we use Harary index to present sufficient conditions for Hamiltonian and Hamilton-connected graphs.

Wiener Index and some Hamiltonian Properties of Graphs

The Wiener index of a connected graph is dened as the sum of distances between all pairs of vertices in the graph. In [9], Yang pre- sented a sucient condition in terms of the Wiener index for a graph to be traceable. Motivated by Yang's result, we present sucient con- ditions based on the Wiener index for a graph to be Hamiltonian or Hamilton-connected in this note, .

Spectral radius and Hamiltonian properties of graphs

Let be a graph with minimum degree . The spectral radius of , denoted by , is the largest eigenvalue of the adjacency matrix of . In this note, we mainly prove the following two results.(1) Let be a graph on vertices with . If , then contains a Hamilton path unless .(2) Let be a graph on vertices with . If , then contains a Hamilton cycle unless . As corollaries of our first result, two previous theorems due to Fiedler and Nikiforov and Lu et al. are obtained, respectively. Our second result refines another previous theorem of Fiedler and Nikiforov.

Distance in Graphs - Taking the Long View

The detour distance between two vertices u and v in a connected graph G is the length of a longest u — v path in G. We survey results and some open questions on detour distance, including connections of this distance to domination, coloring and Hamiltonian properties of graphs.

Hamiltonian properties of graphs with large neighborhood unions

Let G be a graph of order n, σ k = min{ ϵ i=1 k d( ν i ): { ν 1,…, ν k } is an independent set of vertices in G}, NC = min{| N( u)∪ N( ν)|: uν∉ E( G)} and NC2 = min{| N( u)∪ N( ν)|: d( u, ν)=2}. Ore proved that G is hamiltonian if σ 2⩾ n⩾3, while Faudree et al. proved that G is hamiltonian if G is 2-connected and NC⩾ 1 3 (2n−1) . It is shown that both results are generalized by a recent result of Bauer et al. Various other existing results in hamiltonian graph theory involving degree-sums or cardinalities of neighborhood unions are also compared in terms of generality. Furthermore, some new results are proved. In particular, it is shown that the bound 1 3 (2n−1) on NC in the result of Faudree et al. can be lowered to 1 3 (2n−1) , which is best possible. Also, G is shown to have a cycle of length at least min{ n, 2(NC2)} if G is 2-connected and σ 3⩾ n+2. A D λ -cycle ( D λ -path) of G is a cycle (path) C such that every component of G− V( C) has order smaller than λ. Sufficient conditions of Lindquester for the existence of Hamilton cycles and paths involving NC2 are extended to D λ -cycles and D λ -paths.

Forbidden subgraphs and Hamiltonian properties of graphs

Various sufficient conditions are given, in terms of forbidden subgraphs, that imply a graph is either homogeneously traceable, hamiltonian or pancyclic.