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Graphs which have pancyclic complements [PDF]
International Journal of Mathematics and Mathematical Sciences, 1978 Let p and q denote the number of vertices and edges of a graph G, respectively. Let Δ(G) denote the maximum degree of G, and G¯ the complement of G. A graph G of order p is said to be pancyclic if G contains a cycle of each length n, 3≤n≤p.
H. Joseph Straight
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Discussiones Mathematicae Graph Theory, 2015 For integers k and n with 2 ≤ k ≤ n − 1, a graph G of order n is k-path pancyclic if every path P of order k in G lies on a cycle of every length from k + 1 to n. Thus a 2-path pancyclic graph is edge-pancyclic.
Bi Zhenming, Zhang Ping
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Spectral Sufficient Conditions on Pancyclic Graphs
Complexity, 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.
Guidong Yu +3 more
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Hamilton-Connected Mycielski Graphs∗
Discrete Dynamics in Nature and Society, 2021 Jarnicki, Myrvold, Saltzman, and Wagon conjectured that if G is Hamilton-connected and not K2, then its Mycielski graph μG is Hamilton-connected. In this paper, we confirm that the conjecture is true for three families of graphs: the graphs G with δG>VG ...
Yuanyuan Shen +2 more
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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
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Rainbow vertex pair-pancyclicity of strongly edge-colored graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 An edge-colored graph is \emph{rainbow }if no two edges of the graph have the same color. An edge-colored graph $G^c$ is called \emph{properly colored} if every two adjacent edges of $G^c$ receive distinct colors in $G^c$.
Peixue Zhao, Fei Huang
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A Fan-Type Heavy Pair Of Subgraphs For Pancyclicity Of 2-Connected Graphs
Discussiones Mathematicae Graph Theory, 2016 Let G be a graph on n vertices and let H be a given graph. We say that G is pancyclic, if it contains cycles of all lengths from 3 up to n, and that it is H-f1-heavy, if for every induced subgraph K of G isomorphic to H and every two vertices u, v ∈ V (K)
Wideł Wojciech
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Eulerian and pancyclic zero-divisor graphs of ordered sets [PDF]
AKCE International Journal of Graphs and CombinatoricsIn this paper, we determine when the zero-divisor graph of a special class of a finite pseudocomplemented poset is Eulerian. Also, we deal with Hamiltonian, vertex pancyclic, and edge pancyclic properties of the complement of a zero-divisor graph of ...
Nilesh Khandekar, Vinayak Joshi
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Pancyclicity when each Cycle Must Pass Exactly k Hamilton Cycle Chords
Discussiones Mathematicae Graph Theory, 2015 It is known that Θ(log n) chords must be added to an n-cycle to produce a pancyclic graph; for vertex pancyclicity, where every vertex belongs to a cycle of every length, Θ(n) chords are required.
Affif Chaouche Fatima +2 more
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On the Maximal Graph of a Commutative Ring [PDF]
Mathematics Interdisciplinary Research, 2023 Let $R$ be a commutative ring with nonzero identity. Throughout this paper we explore some properties of two certain subgraphs of the maximal graph of $R$.
Masoumeh Soleimani +2 more
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