JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (12): 103-110.doi: 10.6040/j.issn.1671-9352.0.2021.784

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k-Path vertex cover in Cartesian product graphs

SUO Meng-ge, CHEN Jing-rong*, ZHANG Juan-min   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2022-12-05

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Abstract: For a graph G and a positive integer k, a subset S⊆V(G)is called a k-path vertex cover if any path of order k in G contains at least one vertex from S. The cardinality of the minimum k-path vertex cover is called the k-path vertex cover number of graph G, denoted by ψk(G). The k-path vertex cover problem of Cartesian product graphs in cycle graph and cycle graph, cycle graph and complete graph, cycle graph and complete bipartite graph is studied, and the exact value, upper or lower bound of ψk(G)is obtained.

Key words: k-path vertex cover, Cartesian product graph, cycle graph, complete graph, complete bipartite graph

CLC Number: 

  • O157.5
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