Connectivity of Kronecker products with complete multipartite graphs

Wang, Wei; Yan, Zhidan

doi:10.1016/j.dam.2013.01.009

Cited by 7 publications

(6 citation statements)

References 11 publications

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“…To complete our proof for general nilpotent groups, we will make use of work in [16], where the authors study the connectivity of a direct product of a general graph Γ with Algebraic Combinatorics, Vol. 3 #5 (2020) a complete multipartite graph K t1,...,tu under certain restrictions on the parameters t 1 , .…”

Section: Connectivitymentioning

confidence: 99%

Connectivity of generating graphs of nilpotent groups

Harper¹,

Lucchini²

2020

Algebraic Combinatorics

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Let G be 2-generated group. The generating graph Γ(G) is the graph whose vertices are the elements of G and where two vertices g and h are adjacent if G = g, h. This graph encodes the combinatorial structure of the distribution of generating pairs across G. In this paper we study several natural graph theoretic properties related to the connectedness of Γ(G) in the case where G is a finite nilpotent group. For example, we prove that if G is nilpotent, then the graph obtained from Γ(G) by removing its isolated vertices is maximally connected and, if |G| 3, also Hamiltonian. We pose several questions.

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Section: Connectivitymentioning

confidence: 99%

Connectivity of generating graphs of nilpotent groups

Harper¹,

Lucchini²

2020

Algebraic Combinatorics

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show abstract

“…To complete our proof for general nilpotent groups, we will make use of work in [16], where the authors study the connectivity of a direct product of a general graph Γ with a complete multipartite graph K t 1 ,...,tu under certain restrictions on the parameters t 1 , . .…”

Section: Connectivitymentioning

confidence: 99%

Connectivity of generating graphs of nilpotent groups

Harper¹,

Lucchini²

2020

Preprint

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Let G be 2-generated group. The generating graph of Γ(G) is the graph whose vertices are the elements of G and where two vertices g and h are adjacent if G = g, h . This graph encodes the combinatorial structure of the distribution of generating pairs across G. In this paper we study several natural graph theoretic properties related to the connectedness of Γ(G) in the case where G is a finite nilpotent group. For example, we prove that if G is nilpotent, then the graph obtained from Γ(G) by removing its isolated vertices is maximally connected and, if |G| 3, also Hamiltonian. We pose several questions.

show abstract

“…e connectivity of product graphs is well studied. e authors consider the connectivity mainly in [4][5][6] for the Cartesian products, in [7][8][9][10] for the direct products, in [11] for the strong products, and in [12] for the lexicographic products. In almost all cases, more explicit formulae expressed in terms of corresponding graph invariants of factors are obtained; the following result is an example about Cartesian products.…”

Section: Introductionmentioning

confidence: 99%