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.
@article{bwmeta1.element.doi-10_7151_dmgt_1792,
author = {Henry E. Escuadro and Futaba Fujie and Chad E. Musick},
title = {A Note on the Total Detection Numbers of Cycles},
journal = {Discussiones Mathematicae Graph Theory},
volume = {35},
year = {2015},
pages = {237-247},
zbl = {1311.05060},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1792}
}
Henry E. Escuadro; Futaba Fujie; Chad E. Musick. A Note on the Total Detection Numbers of Cycles. Discussiones Mathematicae Graph Theory, Tome 35 (2015) pp. 237-247. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1792/
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