非树序列图的充要条件  

Necessary and sufficient conditions of non-tree sequential graphs

作　　者：朱振广[1] 吴罗义[1] 孙房[1] 

机构地区：[1]辽宁工业大学数理科学系,辽宁锦州121001

出　　处：《辽宁工程技术大学学报（自然科学版）》2009年第4期686-688,共3页Journal of Liaoning Technical University (Natural Science)

基　　金：辽宁省教育厅基金资助项目(05L187)

摘　　要：为处理纠错码问题提供理论基础,使用映射分析、副对角线和邻接矩阵分析的方法,使用"点包"和"1-半副对角线"的概念,获得下列结果:点数大于边数的非树简单图不是序列图;点边数相等的序列图的充要条件;非树序列图的充要条件,及非树序列图有连续的序列标号的充要条件;还给出了方阵的副对角线及半副对角线的结构。这些结果可以用来构造序列图,判别序列图,寻找序列图的序列标号,在通信、军事编码等领域有较大的应用价值。In order to provide a theoretical basis for error-correcting codes, a study was conducted, which applied the methods of mapping analysis, adjacency matrix and semi-diagonal analysis, and the structure of semi-diagonal of square matrix. The study generates following results： 1） the necessary and sufficient conditions of non-tree sequential graphs with equal orders and sizes; 2） the necessary and sufficient conditions of non-tree graphs and non-tree graphs with consecutive sequential labelling. In addition, the relationships among sequential graphs, its vertex closure and the continuous 1-semi- diagonal are found in this study. The non-tree simple graph, which order is great than size, is not sequential graphs. These results can be used to construct sequential graphs, to distinguish sequential graphs and to search for the sequential labelling of a sequential graph.

关 键 词：点包 1-半副对角线 编码 序列标号 序列矩阵 最小边标号 

分 类 号：O157.5[理学—数学]