We consider cubic graphs formed with k ≥ 2 disjoint claws (0 ≤ i ≤ k-1) such that for every integer i modulo k the three vertices of degree 1 of are joined to the three vertices of degree 1 of and joined to the three vertices of degree 1 of . Denote by the vertex of degree 3 of and by T the set . In such a way we construct three distinct graphs, namely FS(1,k), FS(2,k) and FS(3,k). The graph FS(j,k) (j ∈ 1,2,3) is the graph where the set of vertices induce j cycles (note that the graphs FS(2,2p+1), p ≥ 2, are the flower snarks defined by Isaacs [8]). We determine the number of perfect matchings of every FS(j,k). A cubic graph G is said to be 2-factor hamiltonian if every 2-factor of G is a hamiltonian cycle. We characterize the graphs FS(j,k) that are 2-factor hamiltonian (note that FS(1,3) is the “Triplex Graph” of Robertson, Seymour and Thomas [15]). A strong matching M in a graph G is a matching M such that there is no edge of E(G) connecting any two edges of M. A cubic graph having a perfect matching union of two strong matchings is said to be a Jaeger’s graph. We characterize the graphs FS(j,k) that are Jaeger’s graphs.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1495,
author = {Jean-Luc Fouquet and Henri Thuillier and Jean-Marie Vanherpe},
title = {On a family of cubic graphs containing the flower snarks},
journal = {Discussiones Mathematicae Graph Theory},
volume = {30},
year = {2010},
pages = {289-314},
zbl = {1214.05116},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1495}
}
Jean-Luc Fouquet; Henri Thuillier; Jean-Marie Vanherpe. On a family of cubic graphs containing the flower snarks. Discussiones Mathematicae Graph Theory, Tome 30 (2010) pp. 289-314. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1495/
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