Results 41 to 50 of about 1,031 (124)
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
doaj +1 more source
Alternating-Pancyclism in 2-Edge-Colored Graphs
Discussiones Mathematicae Graph Theory, 2021 An alternating cycle in a 2-edge-colored graph is a cycle such that any two consecutive edges have different colors. Let G1, . . ., Gkbe a collection of pairwise vertex disjoint 2-edge-colored graphs. The colored generalized sum of G1, . . ., Gk, denoted
Cordero-Michel Narda +1 more
doaj +1 more source
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
wiley +1 more source
Pancyclism in hamiltonian graphs
Discrete Mathematics, 1991 AbstractWe prove the following theorem. If G is a hamiltonian, nonbipartite graph of minimum degree at least (2n+1)5, where n represents the order of G, then G is pancyclic.
Denise Amar +3 more
openaire +2 more sources
Complement of the generalized total graph of fields
AKCE International Journal of Graphs and Combinatorics, 2020 Let R be a commutative ring and H be a multiplicative prime subset of R. The generalized total graph is the undirected simple graph with vertex set R and two distinct vertices x and y are adjacent if For a field F, is the only multiplicative prime subset
T. Tamizh Chelvam, M. Balamurugan
doaj +1 more source
Locally Pancyclic Graphs [PDF]
Journal of Combinatorial Theory, Series B, 1999 AbstractWe prove the following theorem. LetGbe a graph of ordernand letW⊆V(G). If |W|⩾3 anddG(x)+dG(y)⩾nfor every pair of non-adjacent verticesx, y∈W, then eitherGcontains cyclesC3, C4, …, C|W|such thatCicontains exactlyivertices fromW(i=3, 4, …, |W|), or |W|=nandG=Kn/2, n/2, or else |W|=4,G[W]=K2, 2. This generalizes a result of J. A.
openaire +1 more source
Fan's condition on induced subgraphs for circumference and pancyclicity [PDF]
Opuscula Mathematica, 2017 Let \(\mathcal{H}\) be a family of simple graphs and \(k\) be a positive integer. We say that a graph \(G\) of order \(n\geq k\) satisfies Fan's condition with respect to \(\mathcal{H}\) with constant \(k\), if for every induced subgraph \(H\) of \(G ...
Wojciech Wideł
doaj +1 more source
Edge-pancyclicity of coupled graphs [PDF]
Discrete Applied Mathematics, 2002 AbstractThe coupled graph c(G) of a plane graph G is the graph defined on the vertex set V(G)∪F(G) so that two vertices in c(G) are joined by an edge if and only if they are adjacent or incident in G. We prove that the coupled graph of a 2-connected plane graph is edge-pancyclic.
Ko-Wei Lih +3 more
openaire +1 more source
Local properties of graphs that induce global cycle properties [PDF]
Opuscula MathematicaA graph \(G\) is locally Hamiltonian if \(G[N(v)]\) is Hamiltonian for every vertex \(v\in V(G)\). In this note, we prove that every locally Hamiltonian graph with maximum degree at least \(|V(G)| - 7\) is weakly pancyclic.
Yanyan Wang, Xiaojing Yang
doaj +1 more source
Forbidden Pairs and (k,m)-Pancyclicity
Discussiones Mathematicae Graph Theory, 2017 A graph G on n vertices is said to be (k, m)-pancyclic if every set of k vertices in G is contained in a cycle of length r for each r ∈ {m, m+1, . . . , n}.
Crane Charles Brian
doaj +1 more source