A Note on the Total Detection Numbers of Cycles

• Autorzy: Henry E. Escuadro , Futaba Fujie , Chad E. Musick
• Języki publikacji: 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.

Słowa kluczowe

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2015
• Tom: 35
• Numer: 2
• Strony: 237-247

Daty

wydano

2015-05-01

otrzymano

2013-12-09

poprawiono

2014-05-22

zaakceptowano

2014-05-26

online

2015-04-18

Twórcy

autor

Henry E. Escuadro

• Mathematics Department, Juniata College Huntingdon, PA 16652, USA

autor

Futaba Fujie

• Graduate School of Mathematics, Nagoya University Nagoya, 464-8602, Japan

autor

Chad E. Musick

• Graduate School of Mathematics, Nagoya University Nagoya, 464-8602, Japan

Bibliografia

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• [6] G. Chartrand, L. Lesniak and P. Zhang, Graphs and Digraphs (CRC Press, Boca Raton, FL, 2010).
• [7] H. Escuadro, F. Fujie and C.E. Musick, On the total detection numbers of complete bipartite graphs, Discrete Math. 313 (2013) 2908-2917. doi:10.1016/j.disc.2013.09.001[Crossref]
• [8] H. Escuadro and F. Fujie-Okamoto, The total detection numbers of graphs, J. Com- bin. Math. Combin. Comput. 81 (2012) 97-119.

Identyfikatory

DOI

10.7151/dmgt.1792