The smallest degree sum that yields graphic sequences with a Z3-connected realization

A non-increasing sequence π=(d1,d2,…,dn) of non-negative integers is said to be graphic if it is the degree sequence of a simple graph G on n vertices. Let A be an (additive) Abelian group. An extremal problem for a graphic sequence to have an A-connected realization is considered as follows: determine the smallest even integer σ(A,n) such that each graphic sequence π=(d1,d2,…,dn) with dn≥2 and σ(π)=d1+d2+⋯+dn≥σ(A,n) has an A-connected realization. In this paper, we determine σ(Z3,n) for n≥5.