Matchings in m-generalized fullerene graphs

Behmaram, Afshin; Došlić, Tomislav; Friedland, Shmuel

doi:10.26493/1855-3974.882.539

Cited by 9 publications

(10 citation statements)

References 20 publications

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“…Computing explicitly the reduced form of A for m = 3, 4 and 5, the authors of [Behmaram et al(2016) Behmaram, Došlić, and Friedland] gave an exact formula for Φ(F (3, k), Φ(F (4, k), and Φ(F (5, k):…”

Section: The Transfer Matrix Methodsmentioning

confidence: 99%

“…Theorem 3.1 ( [Behmaram et al(2016) Behmaram, Došlić, and Friedland]). let Φ(F (m, k)) denote the number of perfect matching in F (m, k) then for m=3,4,5 we have:…”

Section: The Transfer Matrix Methodsmentioning

confidence: 99%

“…For example Kutnar and Marušič in [Kutnar and Marušič(2008)] studied Hamiltonicity and cyclic edge-conectivity of F (5, k). See also [Behmaram et al(2016) Behmaram, Došlić, and Friedland] for some structural results about m-barrel fullerene graphs, such as the diameter, Hamiltonicity and the leapfrog transformation.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic enumeration of perfect matchings in m-barrel fullerene graphs

Behmaram

Boutillier²

2019

Discrete Applied Mathematics

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Section: The Transfer Matrix Methodsmentioning

confidence: 99%

“…Theorem 3.1 ( [Behmaram et al(2016) Behmaram, Došlić, and Friedland]). let Φ(F (m, k)) denote the number of perfect matching in F (m, k) then for m=3,4,5 we have:…”

Section: The Transfer Matrix Methodsmentioning

confidence: 99%

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Asymptotic enumeration of perfect matchings in m-barrel fullerene graphs

Behmaram

Boutillier²

2019

Discrete Applied Mathematics

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“…Therefore, it would be interesting to know, which fullerenes are ndistance-balanced at least for some values of n (for example, for n ∈ {1, 2, D}, where D is the diameter of a fullerene in question). For more on fullerenes see [2,5,18].…”

Section: -Distance-balanced Lexicographic Productmentioning

confidence: 99%

On 2-distance-balanced graphs

Frelih

Miklavič

2018

Ars Math. Contemp.

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Let n denote a positive integer. A graph Γ of diameter at least n is said to be n-distancebalanced whenever for any pair of vertices u, v of Γ at distance n, the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. In this article we consider n = 2 (e.g. we consider 2-distance-balanced graphs). We show that there exist 2-distance-balanced graphs that are not 1-distance-balanced (e.g. distance-balanced). We characterize all connected 2-distance-balanced graphs that are not 2-connected. We also characterize 2-distance-balanced graphs that can be obtained as cartesian product or lexicographic product of two graphs.Keywords: n-distance-balanced graph, cartesian product, lexicographic product.Math. Subj. Class.: 05C12, 05C76 Introductory remarksA graph Γ is distance-balanced if for each pair u, v of adjacent vertices of Γ the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. Although these graphs are interesting from the purely graph-theoretical point of view, they also have applications in other areas of research, such as mathematical chemistry and communication networks. It is for that reason that they have been studied from various different points of view in the literature.Distance-balanced graphs were first studied by Handa [9] in 1999. The name distancebalanced, however, was introduced nine years later by Jerebic, Klavžar and Rall [12]. The * We thank the two anonymous referees for many useful comments and suggestions that have greatly improved our initial manuscript, especially for pointing out the mistake in Theorem 5.4.

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“…Previous work on the saturation number includes research on random graphs [8,9], on benzenoid systems [5], fullerenes [1,2,4], and nanotubes [7]. Recent results on related concepts can be found in [3,6].…”

Section: Introductionmentioning

confidence: 99%