Geodetic Number of Powers of Cycles
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 <i>k</i>-th power of a cycl...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2018-11-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/10/11/592 |
| Summary: | 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 <i>k</i>-th power of a cycle. This class of graphs has various applications in Computer Networks design and Distributed computing. The <i>k</i>-th power of a cycle is the graph that has the same set of vertices as the cycle and two different vertices in the <i>k</i>-th power of this cycle are adjacent if the distance between them is at most <i>k</i>. |
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| ISSN: | 2073-8994 |