Results 31 to 40 of about 149 (111)
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
wiley +1 more source
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.
doaj +1 more source
The Complexity of Recognizing Tough Cubic Graphs [PDF]
, 1997 We show that it is NP-hard to determine if a cubic graph G is 1-tough. We then use this result to show that for any integer t # 1, it is NP-hard to determine if a 3 t-regular graph is t-tough. We conclude with some remarks concerning the complexity of
D. Bauer +7 more
core +1 more source
Maximal Independent Sets In Graphs With At Most r Cycles
, 2005 Key Words: cycle, ear decomposition, maximal independent set AMS classification: Primary 05C35; Secondary 05C38, 05C69. We find the maximum number of maximal independent sets in two families of graphs.
Vincent R. Vatter +11 more
core +1 more source
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
core +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
Cyclic Cordial Labeling for the Lemniscate Graphs and Their Second Powers
Journal of Mathematics, Volume 2025, Issue 1, 2025.A lemniscate graph, usually denoted by Ln,m, is defined as a union of two cycles Cn and Cm that share a common vertex. A simple graph is called cyclic group cordial if we can provide a three elements’ cyclic group labeling satisfying certain conditions.
M. A. AbdAllah +4 more
wiley +1 more source
Chordality and 2-Factors in Tough Graphs [PDF]
, 2000 AgraphG is chordal if it contains no chordless cycle of length at least four and is k-chordal if a longest chordless cycle in G has length at most k.Inthis note it is proved that all 3 2 -tough 5-chordal graphs have a 2-factor.
Veldman, H.J. +7 more
core +1 more source