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• # Artykuł - szczegóły

## Discussiones Mathematicae Graph Theory

2015 | 35 | 2 | 237-247

## A Note on the Total Detection Numbers of Cycles

EN

### Abstrakty

EN
Let G be a connected graph of size at least 2 and c :E(G)→{0, 1, . . . , k− 1} an edge coloring (or 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) = (a0, a1, . . . , ak−1), where ai 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 a detectable labeling c of a graph G is the sum of the labels assigned to the edges in G. 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. We investigate the problem of determining the total detection numbers of cycles.

EN

237-247

wydano
2015-05-01
otrzymano
2013-12-09
poprawiono
2014-05-22
zaakceptowano
2014-05-26
online
2015-04-18

### Twórcy

autor
• Mathematics Department, Juniata College Huntingdon, PA 16652, USA
autor
• Graduate School of Mathematics, Nagoya University Nagoya, 464-8602, Japan
autor
• Graduate School of Mathematics, Nagoya University Nagoya, 464-8602, Japan

### Bibliografia

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