Advances and Applications in Discrete Mathematics
Volume 26, Issue 2, Pages 109 - 131
(March 2021) http://dx.doi.org/10.17654/DM026020109 |
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FURTHER RESULTS ON THE UPHILL DOMINATION OF GRAPHS
Thekra Alsalomy, Anwar Saleh, Najat Muthana and Wafa Al Shammakh
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Abstract: A path in a graph is an uphill path if for every A subset is an uphill dominating set “UDS” if every vertex lies on an uphill path originating from some vertex in S. The uphill domination number of G is denoted by and is the minimum cardinality of the UDSs of G. In this paper, we establish the uphill domination number of some families of standard graphs, and obtain some properties of an uphill domination number of graph operations. Also, an upper bound of the uphill domination number for the tensor product of two graphs is found. In addition, we study for Mycielski’s graph. |
Keywords and phrases: uphill path, uphill domination number, Mycielski’s graph.
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