D-Magic Oriented Graphs
Keyword(s):
In this paper, we define D-magic labelings for oriented graphs where D is a distance set. In particular, we label the vertices of the graph with distinct integers {1,2,…,|V(G)|} in such a way that the sum of all the vertex labels that are a distance in D away from a given vertex is the same across all vertices. We give some results related to the magic constant, construct a few infinite families of D-magic graphs, and examine trees, cycles, and multipartite graphs. This definition grew out of the definition of D-magic (undirected) graphs. This paper explores some of the symmetries we see between the undirected and directed version of D-magic labelings.
2018 ◽
Vol 61
(4)
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pp. 848-864
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2009 ◽
Vol 74
(4)
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pp. 1121-1142
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1999 ◽
Vol 8
(1-2)
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pp. 177-184
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1979 ◽
Vol 46
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pp. 125-149
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1977 ◽
Vol 35
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pp. 408-409
1969 ◽
Vol 27
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pp. 12-13