Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4646982 | Discrete Mathematics | 2016 | 9 Pages |
Abstract
Let S=(a1,…,am;b1,…,bn)S=(a1,…,am;b1,…,bn), where a1,…,ama1,…,am and b1,…,bnb1,…,bn are two nonincreasing sequences of nonnegative integers. The pair S=(a1,…,am;b1,…,bn)S=(a1,…,am;b1,…,bn) is said to be a bigraphic pair if there is a simple bipartite graph G=(X∪Y,E)G=(X∪Y,E) such that a1,…,ama1,…,am and b1,…,bnb1,…,bn are the degrees of the vertices in XX and YY, respectively. Let AA be an (additive) Abelian group. We define σ(A,m,n)σ(A,m,n) to be the minimum integer kk such that every bigraphic pair S=(a1,…,am;b1,…,bn)S=(a1,…,am;b1,…,bn) with am,bn≥2am,bn≥2 and σ(S)=a1+⋯+am≥kσ(S)=a1+⋯+am≥k has an AA-connected realization. In this paper, we determine the values of σ(Z3,m,m)σ(Z3,m,m) for m≥4m≥4.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Jian-Hua Yin,