Combinations of some spectral invariants and Hamiltonian properties of graphs

2020 ◽  
Keyword(s):  
Spectral Invariants ◽  
Hamiltonian Properties

scholarly journals Some hamiltonian properties of L1-graphs

2000 ◽  
Vol 223 (1-3) ◽  
pp. 207-216 ◽  
Author(s):  
Rao Li ◽  
R.H. Schelp
Keyword(s):  
Hamiltonian Properties

scholarly journals Hamiltonian Properties of DCell Networks

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

HAMILTONIAN PROPERTIES OF FAULTY RECURSIVE CIRCULANT GRAPHS

2002 ◽  
Vol 03 (03n04) ◽  
pp. 273-289 ◽  
Author(s):  
CHANG-HSIUNG TSAI ◽  
JIMMY J. M. TAN ◽  
YEN-CHU CHUANG ◽  
LIH-HSING HSU
Keyword(s):  
Bipartite Graph ◽  
Hamiltonian Path ◽  
Circulant Graph ◽  
Circulant Graphs ◽  
Vertex Set ◽  
Regular Node ◽  
Hamiltonian Properties

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.

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
Keyword(s):  
Hamiltonian Properties
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