THE STUDY OF ECCENTRICITY SPECTRUM AND ENERGY IN PATH AND CYCLE GRAPHS
Abstract
The eccentricity matrix is one of matrices to represent graphs. The eccentricity matrix is used as a basis for calculating the eccentricity spectrum and energy. This article aims to study the concepts of eccentricity spectrum and energy in simple graphs. For special cases, we also discuss eccentricity spectrum and energy of paths and cycles. All studies in this article focus on providing some examples to facilitate the reader's understanding of the concepts studied. In addition, this article also corrects the mistakes in the lemma about eccentricity spectrum of paths and theorem about eccentricity energy of odd-order cycles from reference articles. Corrections are made by indicating where the errors are in the referenced articles, providing counter examples, correcting inaccurate lemmas and theorems, and giving short proofs. At the end of the article, an open problem is also included to provide an overview of research ideas that can be developed from the concepts of eccentricity spectrum and energy.
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