The k-Path Vertex Cover in Several Cartesian Product Graphs
نویسندگان
چکیده
منابع مشابه
The k-path vertex cover of rooted product graphs
A subset S of vertices of a graph G is called a k-path vertex cover if every path of order k in G contains at least one vertex from S. Denote by ψk(G) the minimum cardinality of a k-path vertex cover in G. In this article a lower and an upper bound for ψk of the rooted product graphs are presented. Two characterizations are given when those bounds are attained. Moreover ψ2 and ψ3 are exactly de...
متن کاملThe k-path vertex cover of some product graphs
For a graph G and a positive integer k, a subset S of vertices of G is called a k-path vertex cover if every path of order k inG contains at least one vertex from S. The cardinality of a minimum k-path vertex cover is denoted by ψk(G). In this paper, we give some bounds and the exact values in special cases for ψk of the Cartesian, and lexicographic products of some graphs. Key–Words: Vertex co...
متن کاملThe k-Path Vertex Cover in Product Graphs of Stars and Complete Graphs∗
For a graph G and a positive integer k, a subset S of vertices of G is called a k-path vertex cover if every path of order k in G contains at least one vertex from S. The cardinality of a minimum k-path vertex cover is denoted by ψk(G). In this paper, we present the exact values of ψk in some product graphs of stars and complete graphs.
متن کاملMinimum k-path vertex cover
A subset S of vertices of a graph G is called a k-path vertex cover if every path of order k in G contains at least one vertex from S. Denote by ψk(G) the minimum cardinality of a k-path vertex cover in G. It is shown that the problem of determining ψk(G) is NP-hard for each k ≥ 2, while for trees the problem can be solved in linear time. We investigate upper bounds on the value of ψk(G) and pr...
متن کاملThe Cover Time of Cartesian Product Graphs
Let P = G H be the cartesian product of graphs G,H. We relate the cover time COV[P ] of P to the cover times of its factors. When one of the factors is in some sense larger than the other, its cover time dominates, and can become of the same order as the cover time of the product as a whole. Our main theorem effectively gives conditions for when this holds. The probabilistic technique which we ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2017
ISSN: 2324-7991,2324-8009
DOI: 10.12677/aam.2017.69143