why is it that edge connectivity is less than or equal to minimum degree of a vertex in graph ?

Question

why is the edge connectivity less than or equal to minimal degree of the vertex , since if we remove the no of edges equal to the minimum degree then the graph will become disconnected so then why is it that we put a less than or equal to condition on edge connectivity ?

Answer 1

i dont know why u r confuse even though u already explained concept..

see Edge connectivity is minimum number of edges removed in order to disconnect a graph. now we have to delete minimum number of edges then try for those vertices which is associated with minimum number of edges i.e. degree of that vertex should be minimum.

 

Note : a bridge in graph results edge connectivity to 1, which is less than minimum degree of any vertex.

Comments

Ya that bridge point was a good point but still what is the trivial case in which edge connectivity is less than minimum no of edges ,can we consider the case of a  graph with a single vertex and a self loop on it ?