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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oai:animorepository.dlsu.edu.ph:etd_bachelors-57822021-04-16T03:22:59Z On the energy of some special classes of graphs Angala, Bianca Marie P. Laforteza, Eryn Grace M. 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. 2010-01-01T08:00:00Z text https://animorepository.dlsu.edu.ph/etd_bachelors/5332 Bachelor's Theses English Animo Repository Graph theory Mathematics |
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Graph theory Mathematics |
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Graph theory Mathematics Angala, Bianca Marie P. Laforteza, Eryn Grace M. On the energy of some special classes of graphs |
| description |
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. |
| format |
text |
| author |
Angala, Bianca Marie P. Laforteza, Eryn Grace M. |
| author_facet |
Angala, Bianca Marie P. Laforteza, Eryn Grace M. |
| author_sort |
Angala, Bianca Marie P. |
| title |
On the energy of some special classes of graphs |
| title_short |
On the energy of some special classes of graphs |
| title_full |
On the energy of some special classes of graphs |
| title_fullStr |
On the energy of some special classes of graphs |
| title_full_unstemmed |
On the energy of some special classes of graphs |
| title_sort |
on the energy of some special classes of graphs |
| publisher |
Animo Repository |
| publishDate |
2010 |
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https://animorepository.dlsu.edu.ph/etd_bachelors/5332 |
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1772834535648526336 |