Results 21 to 30 of about 878 (132)
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
wiley +1 more source
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
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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
wiley +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
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Discrete Applied Mathematics, 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Randerath, Bert +3 more
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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
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Journal of Combinatorial Theory, Series B, 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bollobás, Béla, Thomason, Andrew
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On regular subgraphs of augmented cubes
AKCE International Journal of Graphs and Combinatorics, 2020 The n-dimensional augmented cube AQn is a variation of the hypercube It is a -regular and -connected graph on vertices. One of the fundamental properties of AQn is that it is pancyclic, that is, it contains a cycle of every length from 3 to In this paper,
Amruta Shinde, Y. M. Borse
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Journal of Combinatorial Theory, Series B, 1976 Abstract A graph G with vertex set V(G) and edge set E(G) is pancyclic if it contains cycles of all lengths l, 3 ≤ l ≤ | V(G) |. Theorem . Let G be Hamiltonian and suppose that |E(G)| ≥ n 2 4 , where n = |V(G)|. Then G is either pancyclic or else is the complete bipartite graph K n 2 , n 2 .
Bondy, J.A, Ingleton, A.W
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