Results 51 to 60 of about 1,699 (154)
A Note on Long non-Hamiltonian Cycles in One Class of Digraphs
, 2012 Let $D$ be a strong digraph on $n\geq 4$ vertices. In [3, Discrete Applied Math., 95 (1999) 77-87)], J. Bang-Jensen, Y. Guo and A. Yeo proved the following theorem: if (*) $d(x)+d(y)\geq 2n-1$ and $min \{d^+(x)+ d^-(y),d^-(x)+ d^+(y)\}\geq n-1$ for every
Darbinyan, S. Kh., Karapetyan, I. A.
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Journal of Combinatorial Theory, Series B, 1999 It was shown by \textit{J. A. Bondy} [Stud. Sci. Math. Hung. 4, 473-475 (1969; Zbl 0184.27702)] that if \(G\) is a graph of order \(n\) in which \(d_G(x) + d_G(y) \geq n\) for each pair of nonadjacent vertices \(x\) and \(y\) of \(G\), then \(G\) is either pancyclic or the complete bipartite graph \(K_{n/2,n/2}\).
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An Efficient Hierarchy Algorithm for Community Detection in Complex Networks
Mathematical Problems in Engineering, Volume 2014, Issue 1, 2014., 2014 Community structure is one of the most fundamental and important topology characteristics of complex networks. The research on community structure has wide applications and is very important for analyzing the topology structure, understanding the functions, finding the hidden properties, and forecasting the time‐varying of the networks.
Lili Zhang +5 more
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On pancyclism in hamiltonian graphs
Discrete Mathematics, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kouider, Mekkia, Marczyk, Antoni
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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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Cycles and matchings in randomly perturbed digraphs and hypergraphs
, 2016 We give several results showing that different discrete structures typically gain certain spanning substructures (in particular, Hamilton cycles) after a modest random perturbation.
Krivelevich, Michael +2 more
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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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Journal of Combinatorial Theory, Series B, 1971 AbstractA 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)| ≥ n24, where n = |V(G)|. Then G is either pancyclic or else is the complete bipartite graph Kn2,n2.As a corollary to this theorem it is shown that the Ore conditions for a ...
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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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