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 |
| Language: | English |
| Published: |
Animo Repository
2010
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| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/5332 |
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| Institution: | De La Salle University |
| Language: | English |
| 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 ≤ -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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