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The directed distance dimension of oriented graphs

Gary ChartrandMichael RainesPing Zhang — 2000

Mathematica Bohemica

For a vertex v of a connected oriented graph D and an ordered set W = { w 1 , w 2 , , w k } of vertices of D , the (directed distance) representation of v with respect to W is the ordered k -tuple r ( v | W ) = ( d ( v , w 1 ) , d ( v , w 2 ) , , d ( v , w k ) ) , where d ( v , w i ) is the directed distance from v to w i . The set W is a resolving set for D if every two distinct vertices of D have distinct representations. The minimum cardinality of a resolving set for D is the (directed distance) dimension dim ( D ) of D . The dimension of a connected oriented graph need not be defined. Those oriented graphs...

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