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Note on Path-Connectivity of Complete Bipartite Graphs.
- Source :
-
Journal of Interconnection Networks . Mar2022, Vol. 22 Issue 1, p1-5. 5p. - Publication Year :
- 2022
-
Abstract
- For a graph G = (V , E) and a set S ⊆ V (G) of size at least 2 , a path in G is said to be an S -path if it connects all vertices of S. Two S -paths P 1 and P 2 are said to be internally disjoint if E (P 1) ∩ E (P 2) = ∅ and V (P 1) ∩ V (P 2) = S. Let π G (S) denote the maximum number of internally disjoint S -paths in G. The k -path-connectivity π k (G) of G is then defined as the minimum π G (S) , where S ranges over all k -subsets of V (G). In [M. Hager, Path-connectivity in graphs, Discrete Math. 59 (1986) 53–59], the k -path-connectivity of the complete bipartite graph K a , b was calculated, where k ≥ 2. But, from his proof, only the case that 2 ≤ k ≤ min { a , b } was considered. In this paper, we calculate the situation that min { a , b } + 1 ≤ k ≤ a + b and complete the result. [ABSTRACT FROM AUTHOR]
- Subjects :
- *COMPLETE graphs
*BIPARTITE graphs
*GRAPH connectivity
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 02192659
- Volume :
- 22
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Interconnection Networks
- Publication Type :
- Academic Journal
- Accession number :
- 155894476
- Full Text :
- https://doi.org/10.1142/S0219265921420147