What is the minimum number of vertices should the graph have such that

  1. Edge connectivity of graph is 5
  2. Point connectivity of graph is 3
  3. Minimum degree of each vertex is 7.

I found a graph which has 14 vertex and satisfies the above condition. (Two Complete-7 graph connected by 5 edges at 3 vertex). Can we find a graph with lesser vertex. Prove or disprove.

  • $\begingroup$ Are those 3 different exercises or is it one single graph satisfying all 3 conditions? $\endgroup$ – RGS Jan 10 '17 at 20:13
  • $\begingroup$ It is a single graph that has all 3 properties. $\endgroup$ – Shreedhar Bhat Jan 10 '17 at 20:16

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