ABSTRACT : |
In this paper we prove that regular digraphs are Edge product Cordial and Total magic cordial. A digraph G is said to have edge product cordial labeling if there exists a mapping, f:E(G)→{0,1} and induced vertex labeling function f* :V(G)→{0,1} such that for any vertex vi V(G), f* (vi) is the product of the labels of outgoing edges provided the condition │v(0)- v(1)│≤ 1and │e(0)- e(1)│≤ 1 is hold where v(i) is the number of vertices of G having label i under f* and e(i) is the number of edges of G having label i under f for i = 0,1. A digraph G is said to have a total magic cordial labeling with constant C if there exists a mapping f : V(G) E(G)→{0,1} such that for any vertex vi, the sum of the labels of outgoing edges of vi, and the label of itself is a constant C (mod2) provided the condition │g(0)-g(1)│≤1 is hold where g(0) = v(0) + e(0) and g(1) = v(1) + e(1), where v(i),e(i): i {0,1}are the number of vertices and edges labeled with i respectively.
Keywords: Regular digraph, Graph labeling, Edge product cordial and Total magic cordial labeling |
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