A Note on the Total Detection Numbers of Cycles

Henry 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 -