# A Note on the Total Detection Numbers of Cycles

Henry E. Escuadro; Futaba Fujie; Chad E. Musick

Discussiones Mathematicae Graph Theory (2015)

- Volume: 35, Issue: 2, page 237-247
- ISSN: 2083-5892

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topHenry E. Escuadro, Futaba Fujie, and Chad E. Musick. "A Note on the Total Detection Numbers of Cycles." Discussiones Mathematicae Graph Theory 35.2 (2015): 237-247. <http://eudml.org/doc/271101>.

@article{HenryE2015,

abstract = {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.},

author = {Henry E. Escuadro, Futaba Fujie, Chad E. Musick},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {vertex-distinguishing coloring; detectable labeling; detection number; total detection number; Hamiltonian graph},

language = {eng},

number = {2},

pages = {237-247},

title = {A Note on the Total Detection Numbers of Cycles},

url = {http://eudml.org/doc/271101},

volume = {35},

year = {2015},

}

TY - JOUR

AU - Henry E. Escuadro

AU - Futaba Fujie

AU - Chad E. Musick

TI - A Note on the Total Detection Numbers of Cycles

JO - Discussiones Mathematicae Graph Theory

PY - 2015

VL - 35

IS - 2

SP - 237

EP - 247

AB - 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.

LA - eng

KW - vertex-distinguishing coloring; detectable labeling; detection number; total detection number; Hamiltonian graph

UR - http://eudml.org/doc/271101

ER -

## References

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