Discrete Mathematics
A Group-Theoretic Model for Symmetric Interconnection Networks
IEEE Transactions on Computers
Connectivity of iterated line graphs
Discrete Applied Mathematics
The super-connected property of recursive circulant graphs
Information Processing Letters
On the spanning connectivity and spanning laceability of hypercube-like networks
Theoretical Computer Science
Graph Theory
Note: Connectivity of iterated line graphs
Discrete Applied Mathematics
Graphs and Combinatorics
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For an integer $$s0$$ and for $$u,v\in V(G)$$ with $$u\ne v$$, an $$(s;u,v)$$-path-system of G is a subgraph H of G consisting of s internally disjoint (u, v)-paths, and such an H is called a spanning $$(s;u,v)$$-path system if $$V(H)=V(G)$$. The spanning connectivity $$\kappa ^{*}(G)$$ of graph G is the largest integer s such that for any integer k with $$1\le k \le s$$ and for any $$u,v\in V(G)$$ with $$u\ne v$$, G has a spanning ($$k;u,v$$)-path-system. Let G be a simple connected graph that is not a path, a cycle or a $$K_{1,3}$$. The spanning k-connected index of G, written $$s_{k}(G)$$, is the smallest nonnegative integer m such that $$L^m(G)$$ is spanning k-connected. Let $$l(G)=\max \{m:\,G$$ has a divalent path of length m that is not both of length 2 and in a $$K_{3}$$}, where a divalent path in G is a path whose interval vertices have degree two in G. In this paper, we prove that $$s_{3}(G)\le l(G)+6$$. The key proof to this result is that every connected 3-triangular graph is 2-collapsible.