On thel-connectivity of a graph
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For an integerl ≥ 2, thel-connectivity of a graphG is the minimum number of vertices whose removal fromG produces a disconnected graph with at leastl components or a graph with fewer thanl vertices. A graphG is (n, l)-connected if itsl-connectivity is at leastn. Several sufficient conditions for a graph to be (n, l)-connected are established. IfS is a set ofl(≥ 3) vertices of a graphG, then anS-path ofG is a path between distinct vertices ofS that contains no other vertices ofS. TwoS-paths are said to be internally disjoint if they have no vertices in common, except possibly end-vertices. For a given setS ofl ≥ 2 vertices of a graphG, a sufficient condition forG to contain at leastn internally disjointS-paths, each of length at most 2, is established.
KeywordsDistinct Vertex Condition forG
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