The energy of four graphs of some metacyclic 2-groups
Let G be a metacyclic 2-group and gamma_G is the graph of G. The adjacency matrix of gamma_G is a matrix A=[a_ij] consisting of 0's and 1's in which the entry a_ij is 1 if there is an edge between the ith and jth vertices and 0 otherwise. The energy of a graph is the sum of all absolute...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Penerbit UTM Press
2018
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| Subjects: | |
| Online Access: | http://eprints.utm.my/id/eprint/85480/1/NorHanizaSarmin2018_TheEnergyofFourGraphs.pdf http://eprints.utm.my/id/eprint/85480/ http://dx.doi.org/10.11113/mjfas.v14n1.792 |
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| Summary: | Let G be a metacyclic 2-group and gamma_G is the graph of G. The adjacency matrix of gamma_G is a matrix A=[a_ij] consisting of 0's and 1's in which the entry a_ij is 1 if there is an edge between the ith and jth vertices and 0 otherwise. The energy of a graph is the sum of all absolute values of the eigenvalues of the adjacency matrix of the graph. In this paper, the energy of commuting graph, non-commuting graph, conjugate graph and conjugacy class graph of metacyclic 2-groups are presented. The results show that the energy of these graphs of the groups must be an even integer. |
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