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In this paper, we study \(\varphi \) -labeling \(G_\varphi \) on decomposition of complete bipartite graph by special case of star graph. We prove that, if a complete bipartite graph G is isomorphic to its subgraph \(G_\varphi \) , then for any \(K^j_i\) -copies of a complete bipartite graph of G has an \(\varphi \) -labeling. Finally we proved that, the decomposition of complete bipartite graph G into \(K^j_i\) -copies of the subgraph \(G_\varphi \) has a \(\varphi \) -labeling, where the total number of edges \(|E(G_\varphi )|\) of the \(1^{st}\) - \(K^j_i\) -copies is strictly less than the \(|E(G_\varphi )|\) of the \(n\textrm{th}\) - \(K^j_i\) -copies.

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The \(\psi \) -labeling on Decomposition of Complete Bipartite Graphs

  • 会议论文

  • 发表日期：

    2025年

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  • Aronthung S. Odyuo,
  • M. K. Patel

摘要

In this paper, we study \(\varphi \) -labeling \(G_\varphi \) on decomposition of complete bipartite graph by special case of star graph. We prove that, if a complete bipartite graph G is isomorphic to its subgraph \(G_\varphi \) , then for any \(K^j_i\) -copies of a complete bipartite graph of G has an \(\varphi \) -labeling. Finally we proved that, the decomposition of complete bipartite graph G into \(K^j_i\) -copies of the subgraph \(G_\varphi \) has a \(\varphi \) -labeling, where the total number of edges \(|E(G_\varphi )|\) of the \(1^{st}\) - \(K^j_i\) -copies is strictly less than the \(|E(G_\varphi )|\) of the \(n\textrm{th}\) - \(K^j_i\) -copies.