On the distance spectra of m-generation n-prism graph
| Autor: | Fouzul Atik, Priti Prasanna Mondal, Firdoshi Parveen |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | AKCE International Journal of Graphs and Combinatorics, Vol 19, Iss 3, Pp 276-281 (2022) |
| Druh dokumentu: | article |
| ISSN: | 09728600 2543-3474 0972-8600 |
| DOI: | 10.1080/09728600.2022.2137443 |
| Popis: | AbstractThe distance matrix of a simple connected graph G is [Formula: see text] where dij is the length of a shortest path between the ith and jth vertices of G. Eigenvalues of D(G) are called the distance eigenvalues of G. The m-generation n-prism graph or (m, n)-prism graph can be defined in an iterative way where [Formula: see text]-prism graph is an n-vertex cycle. In this paper, we first find the number of zero eigenvalues of the distance matrix of a (m, n)-prism graph. Next, we find some quotient matrix that contains m nonzero distance eigenvalues of a (m, n)-prism graph. Our next result gives the rest of the nonzero distance eigenvalues of a (m, n)-prism graph in terms of distance eigenvalues of a cycle. Finally, we find the characteristic polynomial of the distance matrix of a (m, n)-prism graph. Applying this result, we provide the explicit distance eigenvalues of a [Formula: see text]-prism graph. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|