Results 31 to 40 of about 303 (83)
Graph Invariants and Large Cycles: A Survey
International Journal of Mathematics and Mathematical Sciences, Volume 2011, Issue 1, 2011., 2011 Graph invariants provide a powerful analytical tool for investigation of abstract substructures of graphs. This paper is devoted to large cycle substructures, namely, Hamilton, longest and dominating cycles and some generalized cycles including Hamilton and dominating cycles as special cases. In this paper, we have collected 36 pure algebraic relations
Zh. G. Nikoghosyan, Howard Bell
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Note on Hamiltonicity of Basis Graphs of Even Delta‐Matroids
Journal of Graph Theory, Volume 109, Issue 4, Page 446-453, August 2025.ABSTRACT We show that the basis graph of an even delta‐matroid is Hamiltonian if it has more than two vertices. More strongly, we prove that for two distinct edges e and f sharing a common end, it has a Hamiltonian cycle using e and avoiding f unless it has at most two vertices or it is a cycle of length at most four.
Donggyu Kim, Sang‐il Oum
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Old and new generalizations of line graphs
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 29, Page 1509-1521, 2004., 2004 Line graphs have been studied for over seventy years. In 1932, H. Whitney showed that for connected graphs, edge‐isomorphism implies isomorphism except for K3 and K1,3. The line graph transformation is one of the most widely studied of all graph transformations.
Jay Bagga
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Long cycles in certain graphs of large degree
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 10, Page 691-697, 2000., 2000 Let G be a connected graph of order n and X = {x ∈ V : d(x) ≥ n/2}. Suppose |X| ≥ 3 and G satisfies the modified Fan′s condition. We show that the vertices of the block B of G containing X form a cycle. This generalizes a result of Fan. We also give an efficient algorithm to obtain such a cycle. The complexity of this algorithm is O(n2). In case G is 2‐
Pak-Ken Wong
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On the Clean Graph of Commutative Artinian Rings
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.For a commutative Artinian ring R with unity, the clean graph Cl(R) is a graph with vertices in the form of an ordered pair (e, u), where e is an idempotent and u is a unit of ring R, respectively. Two distinct vertices (e, u) and (f, v) are adjacent in Cl(R) if and only if ef = fe = 0 or uv = vu = 1.
R. Singh +3 more
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Graphs which have pancyclic complements
International Journal of Mathematics and Mathematical Sciences, Volume 1, Issue 2, Page 177-185, 1978., 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. For a nonnegative integer k, a connected graph G is said to be of rank k if q = p − 1 + k.
H. Joseph Straight
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Chv\'atal-Erd\H{o}s condition for pancyclicity
, 2023 An $n$-vertex graph is Hamiltonian if it contains a cycle that covers all of its vertices and it is pancyclic if it contains cycles of all lengths from $3$ up to $n$.
Sudakov, Benny +2 more
core
Graphs with at most two moplexes
Journal of Graph Theory, Volume 107, Issue 1, Page 38-69, September 2024.Abstract A moplex is a natural graph structure that arises when lifting Dirac's classical theorem from chordal graphs to general graphs. The notion is known to be closely related to lexicographic searches in graphs as well as to asteroidal triples, and has been applied in several algorithms related to graph classes, such as interval graphs, claw‐free ...
Clément Dallard +4 more
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Graphs with degree sequence $\{m^{m-1},n^{n-1}\}$ and $\{m^n,n^m\}$ [PDF]
, 2023 In this paper we study the class of graphs $G_{m,n}$ that have the same degree sequence as two disjoint cliques $K_m$ and $K_n$, as well as the class $\overline G_{m,n}$ of the complements of such graphs. We establish various properties of $G_{m,n}$ and $
Brimkov, Boris, Brimkov, Valentin
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Conditions on subgraphs, degrees, and domination for hamiltonian properties of graphs [PDF]
, 2020 Motivated by a hamiltonicity result due to Ageev, involving claw-free graphs with a small domination number, we study analogous conditions that guarantee different types of hamiltonian properties.
Broersma, Hajo; id_orcid +3 more
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