Two new sufficient conditions for Hamilton-connected graphs

AbstractWe present two new sufficient conditions in terms of the spectral radius $$\rho (G)$$ ρ ( G ) guaranteeing that a k-connected graph G is Hamilton-connected, unless G belongs to a collection of exceptional graphs. We use the Bondy–Chvátal closure to characterize these exceptional graphs.

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Sufficient Conditions for Hamiltonicity of Graphs with Respect to Wiener Index, Hyper-Wiener Index, and Harary Index

Journal of Chemistry ◽

10.1155/2019/2047406 ◽

2019 ◽

Vol 2019 ◽

pp. 1-9

Author(s):

Guisheng Jiang ◽

Lifang Ren ◽

Guidong Yu

Keyword(s):

Minimum Degree ◽

Sufficient Conditions ◽

Wiener Index ◽

Bipartite Graphs ◽

Harary Index ◽

Connected Graphs ◽

Hamilton Connected

In this paper, with respect to the Wiener index, hyper-Wiener index, and Harary index, it gives some sufficient conditions for some graphs to be traceable, Hamiltonian, Hamilton-connected, or traceable for every vertex. Firstly, we discuss balanced bipartite graphs with δG≥t, where δG is the minimum degree of G, and gain some sufficient conditions for the graphs to be traceable or Hamiltonian, respectively. Secondly, we discuss nearly balanced bipartite graphs with δG≥t and present some sufficient conditions for the graphs to be traceable. Thirdly, we discuss graphs with δG≥t and obtain some conditions for the graphs to be traceable or Hamiltonian, respectively. Finally, we discuss t-connected graphs and provide some conditions for the graphs to be Hamilton-connected or traceable for every vertex, respectively.

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Sufficient conditions for Hamilton-connected graphs in terms of (signless Laplacian) spectral radius

Linear Algebra and its Applications ◽

10.1016/j.laa.2020.02.022 ◽

2020 ◽

Vol 594 ◽

pp. 205-225

Author(s):

Qiannan Zhou ◽

Ligong Wang ◽

Yong Lu

Keyword(s):

Spectral Radius ◽

Sufficient Conditions ◽

Laplacian Spectral Radius ◽

Connected Graphs ◽

Signless Laplacian Spectral Radius ◽

Signless Laplacian ◽

Hamilton Connected

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The Structure of Locally Finite Two-Connected Graphs

The Electronic Journal of Combinatorics ◽

10.37236/1211 ◽

1995 ◽

Vol 2 (1) ◽

Cited By ~ 12

Author(s):

Carl Droms ◽

Brigitte Servatius ◽

Herman Servatius

Keyword(s):

Connected Graph ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Locally Finite ◽

Connected Graphs ◽

Finite Graphs ◽

Locally Finite Graphs ◽

Necessary And Sufficient ◽

Block Tree ◽

Labeled Tree

We expand on Tutte's theory of $3$-blocks for $2$-connected graphs, generalizing it to apply to infinite, locally finite graphs, and giving necessary and sufficient conditions for a labeled tree to be the $3$-block tree of a $2$-connected graph.

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The Hyper-Zagreb Index and Some Properties of Graphs

Handbook of Research on Advanced Applications of Graph Theory in Modern Society - Advances in Computer and Electrical Engineering ◽

10.4018/978-1-5225-9380-5.ch006 ◽

2020 ◽

pp. 120-134 ◽

Cited By ~ 1

Author(s):

Rao Li

Keyword(s):

Topological Index ◽

Sufficient Conditions ◽

Disjoint Paths ◽

Zagreb Index ◽

Connected Graphs ◽

Second Zagreb Index ◽

Vertex Disjoint ◽

Hamiltonian Properties

Let G = (V(G), E(G)) be a graph. The complement of G is denoted by Gc. The forgotten topological index of G, denoted F(G), is defined as the sum of the cubes of the degrees of all the vertices in G. The second Zagreb index of G, denoted M2(G), is defined as the sum of the products of the degrees of pairs of adjacent vertices in G. A graph Gisk-Hamiltonian if for all X ⊂V(G) with|X| ≤ k, the subgraph induced byV(G) - Xis Hamiltonian. Clearly, G is 0-Hamiltonian if and only if G is Hamiltonian. A graph Gisk-path-coverableifV(G) can be covered bykor fewer vertex-disjoint paths. Using F(Gc) and M2(Gc), Li obtained several sufficient conditions for Hamiltonian and traceable graphs (Rao Li, Topological Indexes and Some Hamiltonian Properties of Graphs). In this chapter, the author presents sufficient conditions based upon F(Gc) and M2(Gc)for k-Hamiltonian, k-edge-Hamiltonian, k-path-coverable, k-connected, and k-edge-connected graphs.

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