0 0 votes Show that a graph G is non-separable iff every vertex pair can be placed in some circuit in G. Graph Theory graph-theory narsingh-deo + – Ayush Upadhyaya 618 views answer comment Share Follow Print See 1 comment 1 1 comment reply Ayush Upadhyaya commented Jun 8, 2018 reply Follow flag I used below points please let me know if I am correct If in a graph every vertex pair can be included in some circuit in G, then we have a circuit or a cycle in this Graph G. That means to visit each and every vertex we have at least two distinct edge-disjoint paths and even if we remove one vertex we can reach all other vertices via another path that we have. So, clearly, vertex connectivity is not one and hence such graph is non-separable. Is my claim correct? 1 1 replyShare Please log in or register to add a comment.
