Results 31 to 40 of about 144 (109)
Discussiones Mathematicae Graph Theory, 2021 Let G be either a complete graph of odd order or a complete bipartite graph in which each vertex partition has an even number of vertices. In this paper, we determine the set of triples (p, q, r), with p, q, r > 0, for which there exists a decomposition ...
Shyu Tay-Woei
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Longest cycles in certain bipartite graphs
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 1, Page 103-106, 1998., 1995 Let G be a connected bipartite graph with bipartition (X, Y) such that |X| ≥ |Y|(≥2), n = |X| and m = |Y|. Suppose, for all vertices x ∈ X and y ∈ Y, dist(x, y) = 3 implies d(x) + d(y) ≥ n + 1. Then G contains a cycle of length 2m. In particular, if m = n, then G is hamiltomian.
Pak-Ken Wong
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Maps preserving matrices of extremal scrambling index
Special Matrices, 2018 In this paper we characterize surjective linear maps on matrices over antinegative semirings that preserve the set of matrices with maximal or minimal positive values of the scrambling index.
Guterman A.E., Maksaev A.M.
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Path decompositions of chains and circuits
International Journal of Mathematics and Mathematical Sciences, Volume 6, Issue 3, Page 521-533, 1983., 1983 Expressions for the path polynomials (see Farrell [1]) of chains and circuits are derived. These polynomials are then used to deduce results about node disjoint path decompositions of chains and circuits. Some results are also given for decompositions in which specific paths must be used.
E. J. Farrell
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Biclique Decompositions and Hermitian Rank [PDF]
, 1999 The Hermitian rank, h(A), of a Hermitian matrix A is defined and shown to equal maxfn+ (A); n \Gamma (A)g, the maximum of the numbers of positive and negative eigenvalues of A.
Valerie L. Watts +6 more
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On the Minimum Number of Spanning Trees in Cubic Multigraphs
Discussiones Mathematicae Graph Theory, 2020 Let G2n, H2n be two non-isomorphic connected cubic multigraphs of order 2n with parallel edges permitted but without loops. Let t(G2n), t (H2n) denote the number of spanning trees in G2n, H2n, respectively. We prove that for n ≥ 3 there is the unique G2n
Bogdanowicz Zbigniew R.
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Matchings Extend to Hamiltonian Cycles in 5-Cube
Discussiones Mathematicae Graph Theory, 2018 Ruskey and Savage asked the following question: Does every matching in a hypercube Qn for n ≥ 2 extend to a Hamiltonian cycle of Qn? Fink confirmed that every perfect matching can be extended to a Hamiltonian cycle of Qn, thus solved Kreweras’ conjecture.
Wang Fan, Zhao Weisheng
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Spectra of Orders for k-Regular Graphs of Girth g
Discussiones Mathematicae Graph Theory, 2021 A (k, g)-graph is a k-regular graph of girth g. Given k ≥ 2 and g ≥ 3, infinitely many (k, g)-graphs of infinitely many orders are known to exist. Our goal, for given k and g, is the classification of all orders n for which a (k, g)-graph of order n ...
Jajcay Robert, Raiman Tom
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On q-Power Cycles in Cubic Graphs
Discussiones Mathematicae Graph Theory, 2017 In the context of a conjecture of Erdős and Gyárfás, we consider, for any q ≥ 2, the existence of q-power cycles (i.e., with length a power of q) in cubic graphs. We exhibit constructions showing that, for every q ≥ 3, there exist arbitrarily large cubic
Bensmail Julien
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Spectra of expansion graphs [PDF]
, 1999 . Replace certain edges of a directed graph by chains and consider the eect on the spectrum of the graph. It is shown that the spectral radius decreases monotonically with the expansion and that, for a strongly connected graph that is not a single cycle,
Hans Schneider +2 more
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