The energy of cayley graphs for symmetric groups of order 24
A Cayley graph of a finite group G with respect to a subset S of G is a graph where the vertices of the graph are the elements of the group and two distinct vertices x and y are adjacent to each other if xy-1 is in the subset S. The subset of the Cayley graph is inverse closed and does not include t...
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Akademi Sains Malaysia
2020
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my.utm.933072021-11-19T03:15:33Z http://eprints.utm.my/id/eprint/93307/ The energy of cayley graphs for symmetric groups of order 24 Fadzil, A. F. A. Sarmin, N. H. Erfanian, A. QA Mathematics A Cayley graph of a finite group G with respect to a subset S of G is a graph where the vertices of the graph are the elements of the group and two distinct vertices x and y are adjacent to each other if xy-1 is in the subset S. The subset of the Cayley graph is inverse closed and does not include the identity of the group. For a simple finite graph, the energy of a graph can be determined by summing up the positive values of the eigenvalues of the adjacency matrix of the graph. In this paper, the graph being studied is the Cayley graph of symmetric group of order 24 where S is the subset of S4 of valency up to two. From the Cayley graphs, the eigenvalues are calculated by constructing the adjacency matrix of the graphs and by using some properties of special graphs. Finally, the energy of the respected Cayley graphs is computed and presented. Akademi Sains Malaysia 2020 Article PeerReviewed application/pdf en http://eprints.utm.my/id/eprint/93307/1/AmiraFadinaAhmad%20Fadzil2020_TheEnergyofCayleyGraphs.pdf Fadzil, A. F. A. and Sarmin, N. H. and Erfanian, A. (2020) The energy of cayley graphs for symmetric groups of order 24. ASM Science Journal, 13 . ISSN 1823-6782 http://dx.doi.org/10.32802/asmscj.2020.sm26(1.22) DOI: 10.32802/asmscj.2020.sm26(1.22) |
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QA Mathematics Fadzil, A. F. A. Sarmin, N. H. Erfanian, A. The energy of cayley graphs for symmetric groups of order 24 |
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A Cayley graph of a finite group G with respect to a subset S of G is a graph where the vertices of the graph are the elements of the group and two distinct vertices x and y are adjacent to each other if xy-1 is in the subset S. The subset of the Cayley graph is inverse closed and does not include the identity of the group. For a simple finite graph, the energy of a graph can be determined by summing up the positive values of the eigenvalues of the adjacency matrix of the graph. In this paper, the graph being studied is the Cayley graph of symmetric group of order 24 where S is the subset of S4 of valency up to two. From the Cayley graphs, the eigenvalues are calculated by constructing the adjacency matrix of the graphs and by using some properties of special graphs. Finally, the energy of the respected Cayley graphs is computed and presented. |
format |
Article |
author |
Fadzil, A. F. A. Sarmin, N. H. Erfanian, A. |
author_facet |
Fadzil, A. F. A. Sarmin, N. H. Erfanian, A. |
author_sort |
Fadzil, A. F. A. |
title |
The energy of cayley graphs for symmetric groups of order 24 |
title_short |
The energy of cayley graphs for symmetric groups of order 24 |
title_full |
The energy of cayley graphs for symmetric groups of order 24 |
title_fullStr |
The energy of cayley graphs for symmetric groups of order 24 |
title_full_unstemmed |
The energy of cayley graphs for symmetric groups of order 24 |
title_sort |
energy of cayley graphs for symmetric groups of order 24 |
publisher |
Akademi Sains Malaysia |
publishDate |
2020 |
url |
http://eprints.utm.my/id/eprint/93307/1/AmiraFadinaAhmad%20Fadzil2020_TheEnergyofCayleyGraphs.pdf http://eprints.utm.my/id/eprint/93307/ http://dx.doi.org/10.32802/asmscj.2020.sm26(1.22) |
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1717093450477731840 |
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13.160551 |