منابع مشابه
Connectivity of Cartesian product graphs
Use vi , i , i , i to denote order, connectivity, edge-connectivity and minimum degree of a graphGi for i=1, 2, respectively. For the connectivity and the edge-connectivity of the Cartesian product graph, up to now, the best results are (G1×G2) 1+ 2 and (G1×G2) 1+ 2. This paper improves these results by proving that (G1×G2) min{ 1+ 2, 2+ 1} and (G1×G2)= min{ 1+ 2, 1v2, 2v1} ifG1 andG2 are conne...
متن کاملRestricted Connectivity of Cartesian Product Graphs
For a connected graph G = (V (G), E(G)), a vertex set S ⊆ V (G) is a k-restricted vertex-cut if G − S is disconnected such that every component of G − S has at least k vertices. The k-restricted connectivity κk(G) of the graph G is the cardinality of a minimum k-restricted vertex-cut of G. In this paper, we give the 3-restricted connectivity and the 4-restricted connectivity of the Cartesian pr...
متن کاملConnectivity and super-connectivity of Cartesian product graphs
This paper determines that the connectivity of the Cartesian product G1 G2 of two graphs G1 and G2 is equal to min{κ1v2, κ2v1, δ1 + δ2}, where vi, κi, δi is the order, the connectivity and the minimum degree of Gi, respectively, for i = 1, 2, and gives some necessary and sufficient conditions for G1 G2 to be maximally connected and super-connected.
متن کاملOn super edge-connectivity of Cartesian product graphs
The super edge-connectivity λ′ of a connected graph G is the minimum cardinality of an edge-cut F in G such that every component of G − F contains at least two vertices. LetGi be a connected graph with order ni , minimum degree δi and edge-connectivity λi for i = 1, 2. This article shows that λ′(G1 × G2) ≥ min{n1 λ2,n2 λ1,λ1 + 2λ2, 2λ1+λ2} forn1,n2 ≥ 3 andλ′(K2×G2) = min{n2, 2λ2}, which general...
متن کاملTwo bounds for generalized 3-connectivity of Cartesian product graphs
The generalized k-connectivity κk(G) of a graphG, which was introduced by Chartrand et al.(1984) is a generalization of the concept of vertex connectivity. Let G and H be nontrivial connected graphs. Recently, Li et al. gave a lower bound for the generalized 3-connectivity of the Cartesian product graph G H and proposed a conjecture for the case that H is 3-connected. In this paper, we give two...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2006
ISSN: 0012-365X
DOI: 10.1016/j.disc.2005.11.010