Bounds on partition dimension of Peterson graphs
| Autor: | Abdul Jalil M. Khalaf, Muhammasd Azeem, Muhammad Faisal Nadeem, Murat Cancan, Mohammad Reza Farahani |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Journal of Information and Optimization Sciences. 42:1569-1588 |
| ISSN: | 2169-0103 0252-2667 |
| Popis: | The distance of a connected, simple graph P is denoted by d(eta(1), eta(2)), which is the length of a shortest path between the vertices eta(1), eta(2) is an element of V(P), where V(P) is the vertex set of P. The l- ordered partition of V(P) is theta = (theta(1), theta(2), ..., theta(t)}. A vertex eta is an element of V(P), and r(eta vertical bar theta) = {d(eta, theta(1)), d(eta, theta(2)), ...., d(eta, theta(t))} be a l - tuple distances, where r(eta vertical bar theta) is the representation of a vertex eta with respect to set theta. If r(eta vertical bar theta) of eta is unique, for every pair of vertices, then theta is the resolving partition set of V(P). The minimum number l in the resolving partition set theta is known as partition dimension (pd(P)). In this paper, we studied the generalized families of Peterson graph, P-lambda,P-lambda-1 and proved that these families have bounded partition dimension. |
| Databáze: | OpenAIRE |
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