ABSTRACT
A -connected graph G is optimally m-restricted edge-connected if its m-restricted edge-connectivity
equals the minimum m-edge-degree
, and super m-restricted edge-connected if all minimum m-restricted edge cuts are trivial. In this study, a bound for the size of graphs with girth greater than any given integer l
is obtained firstly. Then the second minimum degree conditions for optimally and super m-restricted edge-connected graphs with girth greater than l are provided. Furthermore, the relationship between optimally m-restricted edge connectivity and optimally
-restricted edge connectivity is characterized.
Disclosure statement
No potential conflict of interest was reported by the authors.