scholarly journals On sufficient conditions for a graph to be \(k\)-path-coverable, \(k\)-edge-hamiltonian, Hamilton-connected, traceable and \(k^{-}\)-independent

2020 ◽  
Vol 3 (3) ◽  
pp. 66-76
Author(s):  
Junjiang Li ◽  
◽  
Guifu Su ◽  
Huichao Shi ◽  
Fuguo Liu ◽  
...  
Keyword(s):  
Sufficient Conditions ◽  
Inverse Degree ◽  
Hamilton Connected

The inverse degree of a graph was defined as the sum of the inverses of the degrees of the vertices. In this paper, we focus on finding sufficient conditions in terms of the inverse degree for a graph to be \(k\)-path-coverable, \(k\)-edge-hamiltonian, Hamilton-connected and traceable, respectively. The results obtained are not dropped.

scholarly journals Sufficient Spectral Radius Conditions for Hamilton-Connectivity of k-Connected Graphs

2021 ◽  
Author(s):  
Qiannan Zhou ◽  
Hajo Broersma ◽  
Ligong Wang ◽  
Yong Lu
Keyword(s):  
Spectral Radius ◽  
Connected Graph ◽  
Sufficient Conditions ◽  
Connected Graphs ◽  
Hamilton Connected

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.

scholarly journals Wiener-type invariants and Hamiltonian properties of graphs

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4045-4058
Author(s):  
Qiannan Zhou ◽  
Ligong Wang ◽  
Yong Lu
Keyword(s):  
Bipartite Graph ◽  
Connected Graph ◽  
Sufficient Conditions ◽  
General Graph ◽  
Wiener Type ◽  
Hamilton Connected ◽  
Hamiltonian Properties ◽  
Simple Connected Graph

The Wiener-type invariants of a simple connected graph G = (V(G), E(G)) can be expressed in terms of the quantities Wf = ? {u,v}?V(G)f(dG(u,v)) for various choices of the function f(x), where dG(u,v) is the distance between vertices u and v in G. In this paper, we give some sufficient conditions for a bipartite graph to be Hamiltonian or a connected general graph to be Hamilton-connected and traceable from every vertex in terms of the Wiener-type invariants of G or the complement of G.

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

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.

scholarly journals Energy Conditions for Hamiltonicity of Graphs

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Guidong Yu ◽  
Gaixiang Cai ◽  
Miaolin Ye ◽  
Jinde Cao
Keyword(s):  
Bipartite Graph ◽  
Adjacency Matrix ◽  
Hamiltonian Cycle ◽  
Hamiltonian Path ◽  
Sufficient Conditions ◽  
Simple Graph ◽  
Energy Conditions ◽  
Sufficient Condition ◽  
Hamilton Connected

LetGbe an undirected simple graph of ordern. LetA(G)be the adjacency matrix ofG, and letμ1(G)≤μ2(G)≤⋯≤μn(G)be its eigenvalues. The energy ofGis defined asℰ(G)=∑i=1n‍|μi(G)|. Denote byGBPTa bipartite graph. In this paper, we establish the sufficient conditions forGhaving a Hamiltonian path or cycle or to be Hamilton-connected in terms of the energy of the complement ofG, and give the sufficient condition forGBPThaving a Hamiltonian cycle in terms of the energy of the quasi-complement ofGBPT.

Some Contributions to the Theory of Near-Critical Bisexual Branching Processes

2007 ◽  
Vol 44 (02) ◽  
pp. 492-505
Author(s):  
M. Molina ◽  
M. Mota ◽  
A. Ramos
Keyword(s):  
Branching Process ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Positive Probability ◽  
Limit Laws ◽  
Bisexual Branching Processes ◽  
Probabilistic Evolution

We investigate the probabilistic evolution of a near-critical bisexual branching process with mating depending on the number of couples in the population. We determine sufficient conditions which guarantee either the almost sure extinction of such a process or its survival with positive probability. We also establish some limiting results concerning the sequences of couples, females, and males, suitably normalized. In particular, gamma, normal, and degenerate distributions are proved to be limit laws. The results also hold for bisexual Bienaymé–Galton–Watson processes, and can be adapted to other classes of near-critical bisexual branching processes.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Normal approximations to discrete unimodal distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray
Keyword(s):  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Hypergeometric Distribution ◽  
Death Process ◽  
Normal Approximations ◽  
Discrete Random Variables ◽  
Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

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