Results 31 to 40 of about 1,031 (124)
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
wiley +1 more source
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
wiley +1 more source
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
wiley +1 more source
Some spectral sufficient conditions for a graph being pancyclic
AIMS Mathematics, 2020 Let $G(V,E)$ be a simple connected graph of order $n$. A graph of order $n$ is called pancyclic if it contains all the cycles $C_k$ for $k\in \{3,4,\cdot\cdot\cdot,n\}$. In this paper, some new spectral sufficient conditions for the graph to be pancyclic
Huan Xu +5 more
doaj +1 more source
A Note on Cycles in Locally Hamiltonian and Locally Hamilton-Connected Graphs
Discussiones Mathematicae Graph Theory, 2020 Let 𝒫 be a property of a graph. A graph G is said to be locally 𝒫, if the subgraph induced by the open neighbourhood of every vertex in G has property 𝒫. Ryjáček conjectures that every connected, locally connected graph is weakly pancyclic.
Tang Long, Vumar Elkin
doaj +1 more source
Discrete Applied Mathematics, 1999 AbstractLet G be a graph of order n. A graph G is called pancyclic if it contains a cycle of length k for every 3⩽k⩽n, and it is called vertex pancyclic if every vertex is contained in a cycle of length k for every 3⩽k⩽n. In this paper, we shall present different sufficient conditions for graphs to be vertex pancyclic.
Ingo Schiermeyer +3 more
openaire +3 more sources
Pancyclic subgraphs of random graphs [PDF]
Journal of Graph Theory, 2011 AbstractAn n‐vertex graph is called pancyclic if it contains a cycle of length t for all 3≤t≤n. In this article, we study pancyclicity of random graphs in the context of resilience, and prove that if p>n−1/2, then the random graph G(n, p) a.a.s.
Choongbum Lee, Wojciech Samotij
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Hamiltonicity, independence number, and pancyclicity [PDF]
, 2011 A graph on n vertices is called pancyclic if it contains a cycle of length l for all 3 \le l \le n. In 1972, Erdos proved that if G is a Hamiltonian graph on n > 4k^4 vertices with independence number k, then G is pancyclic.
Lee, Choongbum, Sudakov, Benny
core +2 more sources
The cubic power graph of finite abelian groups
AKCE International Journal of Graphs and Combinatorics, 2021 Let G be a finite abelian group with identity 0. For an integer the additive power graph of G is the simple undirected graph with vertex set G in which two distinct vertices x and y are adjacent if and only if x + y = nt for some with When the additive ...
R. Raveendra Prathap, T. Tamizh Chelvam
doaj +1 more source
On pancyclism in hamiltonian graphs
Discrete Mathematics, 2002 AbstractWe investigate the set of cycle lengths occurring in a hamiltonian graph with at least one or two vertices of large degree. We prove that in every case this set contains all the integers between 3 and some t, where t depends on the order of the graph and the degrees of vertices.
Mekkia Kouider, Antoni Marczyk
openaire +2 more sources