منابع مشابه
The Connectivity of addition Cayley graphs
For any finite abelian group G and any subset S ⊆ G, we determine the connectivity of the addition Cayley graph induced by S on G. Moreover, we show that if this graph is not complete, then it possesses a minimum vertex cut of a special, explicitly described form.
متن کاملSome properties of unitary addition Cayley graphs
Let Γ be an abelian group and B be a subset of Γ. The addition Cayley graph G′ = Cay(Γ, B) is the graph having the vertex set V (G′) = Γ and the edge set E(G′) = {ab : a + b ∈ B}, where a, b ∈ Γ. For a positive integer n > 1, the unitary addition Cayley graph Gn is the graph whose vertex set is Zn, the integers modulo n and if Un denotes set of all units of the ring Zn, then two vertices a, b a...
متن کاملConnectivity of Cayley Graphs: A Special Family
Taking any finite group G, let H ⊂ G be such that 1 6∈ H (where 1 represents the identity element of G) and h ∈ H implies h−1 ∈ H. The Cayley graph X(G;H) is the graph whose vertices are labelled with the elements of G, in which there is an edge between two vertices g and gh if and only if h ∈ H. The exclusion of 1 from H eliminates the possibility of loops in the graph. The inclusion of the in...
متن کاملBounding neighbor-connectivity of Abelian Cayley graphs
For the notion of neighbor-connectivity in graphs whenever a vertex is subverted the entire closed neighborhood of the vertex is deleted from the graph. The minimum number of vertices whose subversion results in an empty, complete, or disconnected subgraph is called the neighborconnectivity of the graph. Gunther, Hartnell, and Nowakowski have shown that for any graph, neighbor-connectivity is b...
متن کاملConnectivity and Planarity of Cayley Graphs
The question of which groups admit planar Cayley graphs goes back over 100 years, being settled for finite groups by Maschke in 1896. Since that time, various authors have studied infinite planar Cayley graphs which satisfy additional special conditions. We consider the question of which groups possess any planar Cayley graphs at all by categorizing such graphs according to their connectivity. ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2009
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2008.06.003