Affiliations: [a] School of Applied Mathematics, Xiamen University of Technology, Xiamen Fujian, People’s Republic of China
| [b] School of Science, Jimei University, Xiamen, People’s Republic of China
Correspondence:
[*]
Corresponding author. Bernard L.S. Lin, School of Science, Jimei University, Xiamen 361021, People’s Republic of China. E-mail: [email protected].
Abstract: Let G = (V, E) be a connected graph. An edge set S ⊂ E is a 3-restricted edge cut, if G - S is disconnected and every component of G - S has at least three vertices. The 3-restricted edge connectivity λ3 (G) of G is the cardinality of a minimum restricted edge cut of G. A graph G is λ3-connected, if 3-restricted edge cuts exist. A graph G is called λ′-optimal, if λ3 (G) = ξ3 (G), where
ξ3(G)=min{|[X,X¯]|:X⊂V,|X|=3,G[X]
is connected}. Furthermore, if every minimum 3-restricted edge cut is a set of edges incident to a set of three vertices, then G is said to be super 3-restricted edge connected or super-λ3 for simplicity. Inverse degree of G is
R(G)=∑v∈V1d(v)
, where d (v) denotes the degree of the vertex v. In this paper, we study the relation of inverse degree and super 3-restricted edge connected graphs.
