Computer Science ›› 2020, Vol. 47 ›› Issue (11A): 444-448.

• Big Data & Data Science •

### Dominating Set Algorithm for Graphs Based on Vertex Order

WANG Hong, GUANG Li-he

1. School of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,China
• Online:2020-11-15 Published:2020-11-17
• About author:WANG Hong,born in 1995,postgra-duate.His main research interests include rough set theory,graph theory and its applications.
GUAN Li-he,born in 1975,Ph.D,associate professor.His main research inte-rests include rough set,data mining and knowledge acquisition.
• Supported by:
This work was supported by the National Natural Science Foundation of China (61573076) and Chongqing ScienceTechnology Commission Project (cstc2015shmszx30004).

Abstract: This paper introduces the attribute order in rough set theory into graph theory,and studies the dominating set problem of undirected graphs based on vertex order.First,a total order relation is defined on the vertex set of graph,which is called vertex order.Then,a binary equivalence relation is defined by using the vertex order,and a partition of closed sets of all vertices in graph is obtained.Finally,based on the partition,a minimal dominating set algorithm for graphs under vertex order is designed.At the same time,it proves the completeness and uniqueness of this algorithm for solving the minimum dominating set under a given vertex order.An example is used to show the correctness and effectiveness of the algorithm.

CLC Number:

• TP18
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