Spectra of Graphs with End Vertices Appended to All Vertices of the Base Graph: The Golden Ratio and Energy

Paul August Winter and Carol Lynne Jessop
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Paul August Winter: Research Asscoiate, University of KwaZulu Natal, Durban, South Africa
Carol Lynne Jessop: Ph.D. Student, University of KwaZulu Natal, Durban, South Africa

Academic Journal of Applied Mathematical Sciences, 2016, vol. 2, issue 7, 56-69

Abstract: In this paper, we determine the spectra of graphs obtained by appending h  end vertex to all vertices of a defined class of graphs called the base graph. The end vertices allow for a quick solution to the eigen-vector equations satisfying the characteristic equation, and the solutions to the eigenvalues of the base graph arise. We determine the relationship between the eigenvalues of the base graph and the eigenvalues of the new graph as constructed above, and determine that if  a  is an eigenvalue of the base .........Â

Keywords: Spectra of graphs; Golden ratio; Graphs with small number of distinct eigenvalues; Graphs with many end vertices; Energy of graphs. (search for similar items in EconPapers)
Date: 2016
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