The edge-connectivity of a connected vertex-transitive graph is equal to the degree d, while the vertex-connectivity will be at least 2(d + 1)/3. If the degree is 4 or less, or the graph is also edge-transitive, or the graph is a minimal Cayley graph, then the vertex-connectivity will also be equal to d.
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A graph is said to be super-connected if every minimum vertex cut isolates a vertex. A graph is said to be hyper-connected if each minimum vertex cut ...
The conditions imposed by edge-transitivity and vertex-transitivity on the connectivity of simple graphs are investigated.
Jul 15, 2022 · A classic theorem of Mader asserts that every connected vertex-transitive graph is maximally edge-connected. We generalise this result to ...
It is well- known [12, 13] that the edge-connectivity of a vertex-transitive graph is equal to its degree. The restricted edge-connectivity of vertex-transitive ...
Jan 24, 2013 · If G is a connected vertex-transitive graph then it is well known that the edge connectivity of G, κ′(G) equals to val(G) - the degree of a ...
May 2, 2024 · Property of edge-vertex transitive graphs · Let Nkv(G) denote the k'th neighbour of v, i.e. vertices which is connected with v by a k-edges path.
Connectivity of Vertex and Edge Transitive Graphs. - ResearchGate
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Oct 22, 2024 · A graph is said to be super-connected if every minimum vertex cut isolates a vertex. A graph is said to be hyper-connected if each minimum ...
The vertex connectivity of an edge-transitive graph always equals its minimum degree. See also. edit · Edge-transitive (in geometry). References. edit. ^ Jump ...
Connectivity of vertex and edge transitive graphs. A graph is said to be super-connected if every minimum vertex cut isolates a vertex. A graph is said to be ...