Mathematics Interdisciplinary Research

Mathematics Interdisciplinary Research

Dominating Set for Bipartite Graph Γ(v, k, l, 2)

Document Type : Original Scientific Paper

Authors
Abolfazl Bahmani 1
Mojgan Emami 2
Ozra Naserian 3
1 Department of mathematics, University of Zanjan, Zanjan, Iran
2 Department of Mathematics, University of Zanjan, Zanjan, Iran
3 Department of Mathematics, Islamic Azad University, Zanjan, Iran
10.22052/mir.2022.246511.1360
Abstract
A bipartite graph (X, Y ) in which X and Y are, respectively, the set of
all l-subsets and all k-subsets of a v-set V as vertices and two vertices being
adjacent if they have i elements in common, is denoted by Γ(v, k, l, i). In
this paper, using the structure of Stiener triple systems, we give dominating
sets for Γ(v, k, l, 2), where 4 ≤ k ≤ 6 and 3 ≤ l ≤ 5.
Keywords
Dominating set
Bipartite graph
Steiner triple system
Subjects
[1] I. Anderson, Combinatorial Designs and Tournaments, Oxford University
Press, 1997.
[2] D. B. West, Introduction to Graph Theory, 2nd Edition, Prentice Hall, 2001.
[3] W. Fish, N. B. Mumba, E. Mwambene and B. G. Rodrigues, Binary codes
and partial permutation decoding sets from biadjacency matrices of the bipartite
graphs Γ(2k + 1; k; k + 2; 1), Graphs Combin. 33 (2) (2017) 357-368,
https://doi.org/10.1007/s00373-017-1765-8.
Mathematics Interdisciplinary Research
Volume 8, Issue 1
Special Issue: Proceedings of the 27th Iranian Algebra Seminar (IAS27) --- Editors: Reza Sharafdini and Mojtaba Sedaghatjoo
Winter 2023
Pages 19-25