Packings and Coverings of a Graph with 6 Vertices and 7 Edges  

一个六点七边图的填充与覆盖(英文)

作　　者：杜艳可 康庆德 

机构地区：[1]Department of Basic Courses, Ordnance Engineering College [2]Institute of Mathematics, Hebei Normal University

出　　处：《Journal of Mathematical Research and Exposition》2008年第4期799-806,共8页数学研究与评论（英文版）

基　　金：the National Natural Science Foundation of China (No.10671055)

摘　　要：Let λKv be the complete multigraph with v vertices and G a finite simple graph. A G-design (G-packing design, G-covering design) of λKv, denoted by (v,G,λ)-GD ((v,G,λ)-PD, (v,G,λ)-CD), is a pair (X,B) where X is the vertex set of Kv and B is a collection of subgraphs of Kv, called blocks, such that each block is isomorphic to G and any two distinct vertices in Kv are joined in exactly (at most, at least) λ blocks of B. A packing (covering) design is said to be maximum (minimum) if no other such packing (cov...Let λKv be the complete multigraph with v vertices and G a finite simple graph. A G-design (G-packing design, G-covering design) of λKv, denoted by (v,G,λ)-GD ((v,G,λ)-PD, (v,G,λ)-CD), is a pair (X,B) where X is the vertex set of Kv and B is a collection of subgraphs of Kv, called blocks, such that each block is isomorphic to G and any two distinct vertices in Kv are joined in exactly (at most, at least) λ blocks of B. A packing (covering) design is said to be maximum (minimum) if no other such packing (covering) design has more (fewer) blocks. In this paper, a simple graph G with 6 vertices and 7 edges is discussed, and the maximum G-PD(v) and the minimum G-CD(v) are constructed for all orders v.

关 键 词：G-design G-packing design G-covering design. 

分 类 号：O157.5[理学—数学]