On totally antimagic total labeling of complete bipartite graphs
Abolape D. Akwu, Deborah O. A. Ajayi
TL;DR
This paper proves that complete bipartite graphs and their joins with a single vertex are totally antimagic total graphs, expanding the class of graphs known to have such labelings.
Contribution
It establishes that all complete bipartite graphs and their joins with one vertex are totally antimagic total graphs, filling a gap in graph labeling theory.
Findings
Complete bipartite graphs are totally antimagic total graphs.
Join of complete bipartite graphs with one vertex is totally antimagic total.
The paper provides constructive proofs for these properties.
Abstract
This paper deals with the problem of finding totally antimagic total labelings of complete bipartite graphs. We prove that complete bipartite graphs are totally antimagic total graphs. We also show that the join of complete bipartite graphs with one vertex is a totally antimagic total graph
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Taxonomy
TopicsGraph Labeling and Dimension Problems · graph theory and CDMA systems