On the energy of some special classes of graphs
This study is an exposition of the article called Energy of a Graph is never the square root of an Odd Integer by S. Pirzada and I. Gutman. The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. In this thesis, the theorem initially proved by Bapat and Pati (Bull. Ke...
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| Main Authors: | , |
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| Format: | text |
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Animo Repository
2010
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| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/10853 |
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| Institution: | De La Salle University |
| Summary: | This study is an exposition of the article called Energy of a Graph is never the square root of an Odd Integer by S. Pirzada and I. Gutman. The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. In this thesis, the theorem initially proved by Bapat and Pati (Bull. Kerala Math. Assoc., 1 (2004), 129-134) is included (a) E(G) is never an odd integer. The main objective of this study is to show that (b) E(G) is never the square root of an odd integer. In addition, if r and s are integers such that r ≥ 1 and 0 ≤ s ≤ r – 1 and q is an odd integer, then E(G) cannot be of the form (2sq)1/r, a result that implies (a) and (b) as special cases. |
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