Results 11 to 20 of about 635 (107)
Hamiltonicity of graphs perturbed by a random regular graph
Random Structures &Algorithms, Volume 62, Issue 4, Page 857-886, July 2023., 2023 Abstract We study Hamiltonicity and pancyclicity in the graph obtained as the union of a deterministic n$$ n $$‐vertex graph H$$ H $$ with δ(H)≥αn$$ \delta (H)\ge \alpha n $$ and a random d$$ d $$‐regular graph G$$ G $$, for d∈{1,2}$$ d\in \left\{1,2\right\} $$. When G$$ G $$ is a random 2‐regular graph, we prove that a.a.s.
Alberto Espuny Díaz, António Girão
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Hamiltonicity of graphs perturbed by a random geometric graph
Journal of Graph Theory, Volume 103, Issue 1, Page 12-22, May 2023., 2023 Abstract We study Hamiltonicity in graphs obtained as the union of a deterministic n $n$‐vertex graph H $H$ with linear degrees and a d $d$‐dimensional random geometric graph G d ( n , r ) ${G}^{d}(n,r)$, for any d ≥ 1 $d\ge 1$. We obtain an asymptotically optimal bound on the minimum r $r$ for which a.a.s.
Alberto Espuny Díaz
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Hamilton‐Connected Mycielski Graphs∗
Discrete Dynamics in Nature and Society, Volume 2021, Issue 1, 2021., 2021 Jarnicki, Myrvold, Saltzman, and Wagon conjectured that if G is Hamilton‐connected and not K2, then its Mycielski graph μ(G) is Hamilton‐connected. In this paper, we confirm that the conjecture is true for three families of graphs: the graphs G with δ(G) > |V(G)|/2, generalized Petersen graphs GP(n, 2) and GP(n, 3), and the cubes G3.
Yuanyuan Shen +3 more
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Spectral Sufficient Conditions on Pancyclic Graphs
Complexity, Volume 2021, Issue 1, 2021., 2021 A pancyclic graph of order n is a graph with cycles of all possible lengths from 3 to n. In fact, it is NP‐complete that deciding whether a graph is pancyclic. Because the spectrum of graphs is convenient to be calculated, in this study, we try to use the spectral theory of graphs to study this problem and give some sufficient conditions for a graph to
Guidong Yu +4 more
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Computing Edge Weights of Symmetric Classes of Networks
Mathematical Problems in Engineering, Volume 2021, Issue 1, 2021., 2021 Accessibility, robustness, and connectivity are the salient structural properties of networks. The labelling of networks with numeric numbers using the parameters of edge or vertex weights plays an eminent role in the study of the aforesaid properties.
Hafiz Usman Afzal +4 more
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Enumeration of the Edge Weights of Symmetrically Designed Graphs
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 The idea of super (a, 0)‐edge‐antimagic labeling of graphs had been introduced by Enomoto et al. in the late nineties. This article addresses super (a, 0)‐edge‐antimagic labeling of a biparametric family of pancyclic graphs. We also present the aforesaid labeling on the disjoint union of graphs comprising upon copies of C4 and different trees.
Muhammad Javaid +3 more
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Discrete Applied Mathematics, 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bert Randerath +3 more
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Computing Edge Weights of Magic Labeling on Rooted Products of Graphs
Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 Labeling of graphs with numbers is being explored nowadays due to its diverse range of applications in the fields of civil, software, electrical, and network engineering. For example, in network engineering, any systems interconnected in a network can be converted into a graph and specific numeric labels assigned to the converted graph under certain ...
Jia-Bao Liu +3 more
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Discrete Mathematics, 2001 Suppose \(k\) and \(n\) are integers such that \(3\leq k\leq n\). If \(3\leq k\leq\sqrt{n+1}\), let \(h(k)= (n+ 1)/k+ (k- 4)/2\) if \(k\) is even and let \(h(k)= (n+ 2)/k+ (k-5)/2\) if \(k\) is odd. If \(\sqrt{n+1}< k\leq n\), let \(h(k)= 3n/(2k+ 2)- 1/2\).
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Rainbow Pancyclicity in Graph Systems [PDF]
The Electronic Journal of Combinatorics, 2021 Let $G_1,\ldots,G_n$ be graphs on the same vertex set of size $n$, each graph with minimum degree $\delta(G_i)\ge n/2$. A recent conjecture of Aharoni asserts that there exists a rainbow Hamiltonian cycle i.e. a cycle with edge set $\{e_1,\ldots,e_n\}$ such that $e_i\in E(G_i)$ for $1\leq i \leq n$.
Yangyang Cheng +2 more
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