scholarly journals The Hamiltonian properties of supergrid graphs

2015 ◽  
Vol 602 ◽  
pp. 132-148 ◽  
Author(s):  
Ruo-Wei Hung ◽  
Chih-Chia Yao ◽  
Shang-Ju Chan
2000 ◽  
Vol 223 (1-3) ◽  
pp. 207-216 ◽  
Author(s):  
Rao Li ◽  
R.H. Schelp

2015 ◽  
Vol 58 (11) ◽  
pp. 2944-2955 ◽  
Author(s):  
Xi Wang ◽  
Alejandro Erickson ◽  
Jianxi Fan ◽  
Xiaohua Jia

2002 ◽  
Vol 03 (03n04) ◽  
pp. 273-289 ◽  
Author(s):  
CHANG-HSIUNG TSAI ◽  
JIMMY J. M. TAN ◽  
YEN-CHU CHUANG ◽  
LIH-HSING HSU

We present some results concerning hamiltonian properties of recursive circulant graphs in the presence of faulty vertices and/or edges. The recursive circulant graph G(N, d) with d ≥ 2 has vertex set V(G) = {0, 1, …, N - 1} and the edge set E(G) = {(v, w)| ∃ i, 0 ≤ i ≤ ⌈ log d N⌉ - 1, such that v = w + di (mod N)}. When N = cdk where d ≥ 2 and 2 ≤ c ≤ d, G(cdk, d) is regular, node symmetric and can be recursively constructed. G(cdk, d) is a bipartite graph if and only if c is even and d is odd. Let F, the faulty set, be a subset of V(G(cdk, d)) ∪ E(G(cdk, d)). In this paper, we prove that G(cdk, d) - F remains hamiltonian if |F| ≤ deg (G(cdk, d)) - 2 and G(cdk, d) is not bipartite. Moreover, if |F| ≤ deg (G(cdk, d)) - 3 and G(cdk, d) is not a bipartite graph, we prove a more stronger result that for any two vertices u and v in V(G(cdk, d)) - F, there exists a hamiltonian path of G(cdk, d) - F joining u and v.


Author(s):  
Rao Li

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.


2020 ◽  
Vol 343 (1) ◽  
pp. 111644
Author(s):  
Wei Zheng ◽  
Hajo Broersma ◽  
Ligong Wang ◽  
Shenggui Zhang

1994 ◽  
Vol 35 (8) ◽  
pp. 4067-4087 ◽  
Author(s):  
A. N. Leznov ◽  
A. V. Razumov

2009 ◽  
Vol 309 (13) ◽  
pp. 4608-4613 ◽  
Author(s):  
Gek L. Chia ◽  
Siew-Hui Ong ◽  
Li Y. Tan

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