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The energy of cayley graphs for a generating subset of the dihedral groups

Ahmad Fadzil, Amira Fadina and Sarmin, Nor Haniza and Erfanian, Ahmad (2019) The energy of cayley graphs for a generating subset of the dihedral groups. Matematika: Malaysian Journal Of Industrial And Applied Mathematics, 35 (3). pp. 371-376. ISSN 0127-8274

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Official URL: http://dx.doi.org/10.11113/matematika.v35.n3.1115

Abstract

Let G be a finite group and S be a subset of G where S does not include the identity of G and is inverse closed. A Cayley graph of a group G with respect to the subset S is a graph where its vertices are the elements of G and two vertices a and b are connected if ab^(−1) is in the subset S. The energy of a Cayley graph is the sum of all absolute values of the eigenvalues of its adjacency matrix. In this paper, we consider a specific subset S = {b, ab, . . . , a^(n−1)b} for dihedral group of order 2n, where n is greater or equal to 3 and find the Cayley graph with respect to the set. We also calculate the eigenvalues and compute the energy of the respected Cayley graphs. Finally, the generalization of the energy of the respected Cayley graphs is found.

Item Type:Article
Uncontrolled Keywords:eigenvalues, adjacency matrix
Subjects:Q Science > QA Mathematics
Divisions:Science
ID Code:89553
Deposited By: Widya Wahid
Deposited On:22 Feb 2021 09:47
Last Modified:22 Feb 2021 09:47

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