A graph G is called maximally edge-connected if λ(G)=δ(G) and it is said to be super edge-connected if every minimal edge-cut-set of size δ(G) separates only one isolated point of G.It is proved that for any graph G,G~(-+) is maximally edge-connected and that G~(——+) is super edge-connected if and only if G is neither isomorphic to K_(1,2) nor K_2∪K_1.

Super edge-connectivity of transformation graph G~(——+)

Super Edge-connectivity of Transformation Graphs G -++ .

Calculation and isomorphism is one of the important topics in graph theory. Especially to keep some structure parameters of graph invariant operation is the focus of attention of the structure graph. Study on the transformation graph can study some special graphs and their relationship in a larger range. This paper studied the isomorphism of some kind of transformation graph. By the method of degree sequence, It was shown that two transformation graphs are isomorphic if and only if the two original graphs are isomorphic.

The Isomorphism of Some Kind of Transformation Graph

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The Isomorphism of Some Kind of Transformation Graph