Abstract

The geodetic number of a graph is an important graph invariant. In 2002, Atici showed the geodetic set determination of a graph is an NP-Complete problem. In this paper, we compute the geodetic set and geodetic number of an important class of graphs called the k-th power of a cycle. This class of graphs has various applications in Computer Networks design and Distributed computing. The k-th power of a cycle is the graph that has the same set of vertices as the cycle and two different vertices in the k-th power of this cycle are adjacent if the distance between them is at most k.

Details

Title
Geodetic Number of Powers of Cycles
Author
Abudayah, Mohammad 1 ; Alomari, Omar 1   VIAFID ORCID Logo  ; Hassan Al Ezeh 2 

1  School of Basic Sciences and Humanities, German Jordanian University, Amman 11180, Jordan 
2  Department of Mathematics, The University of Jordan, Amman 11942, Jordan 
First page
592
Publication year
2018
Publication date
2018
Publisher
MDPI AG
e-ISSN
20738994
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.3390/sym10110592
ProQuest document ID
2582928415
Copyright
© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.