IJAM: Volume 38, No. 3 (2025)

DOI: 10.12732/ijam.v38i3.9

ADJACENCY-DISTANCE AND GENERALIZED
ADJACENCY DISTANCE ENERGIES OF
NON-COMMUTING GRAPH FOR
DIHEDRAL GROUPS

 

Mamika Ujianita Romdhini1,ยง, Abdurahim2, Andika Ellena Saufika Hakim Maharani3, Athirah Nawawi4, Faisal Al-Sharqi5, Ifan Hasnan Dani6

 

1,2,3,6 Department of Mathematics
Faculty of Mathematics and Natural Sciences
University of Mataram, Mataram 83125, INDONESIA
4 Department of Mathematics and Statistics
Faculty of Science, Universiti Putra Malaysia
43400 Serdang, Selangor, MALAYSIA
5 Department of Mathematics
Faculty of Education for Pure Sciences
University Of Anbar, Ramadi, Anbar, IRAQ

 

Abstract. The correspondence between matrix and graph is one of the fundamental characteristics of the spectral graph theory. This relation allows us to formulate the characteristic polynomial of the graph and calculate the energy of the graph as the sum of its absolute eigenvalues. This study examines the non-commuting graph for dihedral groups. We establish the spectral radius and energy of this graph using the adjacency-distance and generalized adjacency-distance matrices. It should be noted that the obtained energies are never an odd integer and are always equal to twice its spectral radius.

 

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How to cite this paper?
DOI: 10.12732/ijam.v38i3.9
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2025
Volume: 38
Issue: 3

References

[1] A. Abdollahi, S. Akbari, H. R. Maimani, Non-commuting Graph of a Group, J. Algebra, 298, No 2 (2006), 468-492.

[2] M. Aschbacher, Finite Group Theory, Cambridge University Press, Cambridge (2000).

[3] R. B. Bapat, S. Pati, Energy of a graph is never an odd integer, Bull. Kerala Math. Assoc., 1 (2004), 129-132.

[4] H. Guo, B. Zhou, On adjacency-distance spectral radius and spread of graphs, Appl. Math. Comput., 369 (2020), 124819.

[5] I. Gutman, The energy of graph, Ber. Math. Statist. Sekt. Forschungszenturm Graz, 72 (1978), 1-2.

[6] R. A. Horn, C. A. Johnson, Matrix Analysis, Cambridge University Press, Cambridge (1985).

[7] G. Pasten, O. Rojo, The generalized adjacency-distance matrix of connected graphs, Linear Multilinear Algebra (2023), 1-20.

[8] S. Pirzada, I. Gutman, Energy of a graph is never the square root of an odd integer, Appl. Anal. Discret. Math., 2 (2008), 118-121.

[9] H. S. Ramane, S. S. Shinde, Degree exponent polynomial of graphs obtained by some graph operations, Electron. J. Graph Theory Appl., 63 (2017), 161-168.

[10] M. U. Romdhini, F. Al-Sharqi, A. Nawawi, A. Al-Quran, Closeness Energy of Non-Commuting Graph for Dihedral Groups, Eur. J. Pure Appl. Math., 17, No 1 (2024), 212-221.

[11] M. U. Romdhini, A. Nawawi, On the spectral radius and Sombor energy of the non-commuting graph for dihedral groups, Mal. J. Fund. Appl. Sci., 20 (2024), 65-73.

[12] M. U. Romdhini, A. Nawawi, F. Al-Sharqi, A. Al-Quran, S. R. Kamali, Wiener-Hosoya energy of non-commuting graph for dihedral groups, Asia Pac. J. Math., 11, No 9 (2024), 1-9.

[13] H. P. Schultz, Topological organic chemistry. 1. Graph theory and topological indices of alkanes, J. Chem. Inf. Comput. Sci., 29 (1989), 227-228.

 

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