Vertex-Domatic, Edge-Domatic and Total Domatic Number of Uniform Hypergraphs
Smruti Prava Dash
TL;DR
This paper explores the domatic, edge-domatic, and total domatic numbers in specific uniform hypergraphs, extending previous concepts from graphs to hypergraphs and providing new theoretical insights.
Contribution
It investigates and proves new assertions regarding the vertex, edge, and total domatic numbers in certain uniform hypergraphs, expanding the theoretical framework.
Findings
Established bounds for domatic numbers in uniform hypergraphs
Proved new theorems relating to hypergraph domatic properties
Extended graph domatic concepts to hypergraph contexts
Abstract
E. J. Cockayne and S. T. Hedetniemi introduced the concept of domatic number of a graph. B. Zelinka extended the concept to the uniform hypergraphs. Further, B. Zelinka defined the concept of edge-domatic number and total edge-domatic number of a graph. In this paper, we investigate and prove some assertions in connection with vertex domatic number, edge-domatic number and total domatic number of some specific uniform hypergraphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · graph theory and CDMA systems