The structure and metric dimension of the power graph of a finite group
نویسندگان
چکیده
The power graphPG of a finite group G is the graph with the vertex set G, where two distinct vertices are adjacent if one is a power of the other. We first show that PG has a transitive orientation, so it is a perfect graph and its core is a complete graph. Then we use the poset on all cyclic subgroups of G (under usual inclusion) to characterize the structure ofPG. Finally, a closed formula for themetric dimension of PG is established. As an application, we compute the metric dimension of the power graph of a cyclic group. © 2014 Elsevier Ltd. All rights reserved.
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ورودعنوان ژورنال:
- Eur. J. Comb.
دوره 43 شماره
صفحات -
تاریخ انتشار 2015