The spectrum of the power graph of a cyclic $p-$group and some characteristics of an orthogonal graph in an indefinite metric space
Keywords:
Finite groups, graphs, power graph, adjacency matrix, Laplacian matrix, spectrum of a graph, isomorphic graphs, algebraic connectivity, space with indefinite metric, orthogonal graph
Abstract
In this paper, among other results we find the spectrum of the power graph of a finite cyclic $p-$group, we show that the spectrum of the combinatorial Laplacian of the power graph of a finite group $P(G)$ has exactly $n-1$ positive eigenvalues being $n$ the order of the group $G$, for this the basic concepts of group theory are included, certain theorems that support this study, the concept of graph, the essential results of graph theory, algebraic theory of graph and finally the concept of power graph of a finite group, which was presented for the first time in \cite{Chakrabarty}. Finally, a characterization of the orthogonal graph of an indefinite metric space is made, which was introduced by the researchers in this article.
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References
Chakrabarty, I. and Ghosh, S. and Sen, M.K, {\it Undirected power graphs of semigroups}, Semigroup Forum, vol. 78, Springer, 2009, pp. 410–426.
P. Balakrishnan, M. Sattanathan, and R. Kala, {\it The center graph of a
group}, South Asian J. Math 1 (2011), no. 1
P. Balakrishnan, M. Sattanathan, and R. Kala, {\it The center graph of a
group}, South Asian J. Math 1 (2011), no. 1
Published
2023-12-31
How to Cite
Aldana Palomino, E., Araujo Martinez, C. A., & Barajas, J. D. (2023). The spectrum of the power graph of a cyclic $p-$group and some characteristics of an orthogonal graph in an indefinite metric space. Revista MATUA ISSN: 2389-7422, 10(1), 11-19. Retrieved from https://investigaciones.uniatlantico.edu.co/revistas/index.php/MATUA/article/view/3815
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