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A New Family of Graphs and Strong Antireciprocal Eigenvalue Property

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  • Sadia Akhter
  • G. Muhiuddin
  • Saira Hameed
  • Uzma Ahmad
  • Ammar Alsinai

Abstract

Spectral graph theory explores the relationship between the eigenvalues and the structural properties of graphs. This study focuses on the fundamental matrices associated with simple graphs, specifically the adjacency matrix. This work contributes to the spectral graph theory literature by introducing a new family of simple connected graphs and investigating their eigenvalue properties. We examine conditions under which these graphs satisfy specific spectral properties, such as the strong antireciprocal eigenvalue property. Additionally, we construct another family of graphs from this new family, proving that each graph within this derived family satisfies the strong antireciprocal eigenvalue property. Through these contributions, we aim to deepen the understanding of the spectral characteristics of graph families and their applications in theoretical and applied contexts.

Suggested Citation

  • Sadia Akhter & G. Muhiuddin & Saira Hameed & Uzma Ahmad & Ammar Alsinai, 2024. "A New Family of Graphs and Strong Antireciprocal Eigenvalue Property," Journal of Mathematics, Hindawi, vol. 2024, pages 1-12, July.
    • Handle: RePEc:hin:jjmath:8849362
    DOI: 10.1155/2024/8849362
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