| Popis: |
Let G be a connected graph of size at least 2 and c : E ( G ) → { 0 , 1 , … , k − 1 } an edge labeling of G using k labels, where adjacent edges may be assigned the same label. For each vertex v of G , the color code of v with respect to c is the k -vector code ( v ) = ( a 0 , a 1 , … , a k − 1 ) , where a i is the number of edges incident with v that are labeled i for 0 ≤ i ≤ k − 1 . The labeling c is called a detectable labeling if distinct vertices in G have distinct color codes. The value val ( c ) of an edge labeling c of a graph G is the sum of the labels assigned to the edges in G by c . The total detection number td ( G ) of G is defined by td ( G ) = min { val ( c ) } , where the minimum is taken over all detectable labelings c of G . In this paper, we investigate the total detection numbers of complete bipartite graphs. |
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