A note on the vertex-distinguishing index for some cubic graphs

• Autorzy: Taczuk K. , Woźniak M.
• Języki publikacji: EN

Abstrakty

EN

The vertex-distinguishing index of a graph G (vdi (G)) is the minimum number of colours required to colour properly the edges of a graph in such a way that any two vertices are incident with different sets of colours. We consider this parameter for some families of cubic graphs.

Słowa kluczowe

EN

edge colouring; vertex-distinguishing colouring; cubic graphs

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2004
• Tom: Vol. 24, no. 2
• Strony: 223--229
• Opis fizyczny: Bibliogr. 12 poz., rys.

Twórcy

autor

Taczuk K.

• School of Economics and Computer Science ul. Św. Filipa 17, 31-150 Cracow, Poland

autor

Woźniak M.

• AGH University of Science and Technology Faculty of Applied Mathematics al. Mickiewicza 30, 30-059 Cracow, Poland

Bibliografia

• [1] Balister P. N., Bollobas B., Schelp R.H.: Vertex Distinguishing colourings of Graphs with A(G) = 2. Discrete Math. 252 (2002), 17-29.
• [2] Balister P. N., Kostochka A., Li H., Schelp R. H.: Balanced edge colorings. J. Combin. Theory, Series B 90 (2004), 3-20.
• [3] Balister P. N., Riordan O.M., Schelp R.H.: Vertex Distinguishing edge colorings of graphs. J. Graph Theory 42 (2003), 95-109.
• [4] Bazgan C, Harkat-Benhamdine A., Li H., Woźniak M.:, On the vertex-distinguishing proper edge-colourings of graphs. J. Combin. Theory, Series B 75 (1999), 288-301.
• [5] Bazgan C, Harkat-Benhamdine A., Li H., Woźniak M.: A note on the vertex-distinguishing proper colorings of graphs with large minimum degree. Discrete Math. 236 (2001), 37-42.
• [6] Bondy J. A., Murty U.S.R.: Graph Theory with Applications. London, New York, Elsevier, Macmillan 1976.
• [7] Burris A. C: Vertex-distinguishing edge-colourings. Ph.D. Dissertation, Memphis State University, 1993.
• [8] Burris A. C, Schelp R.H.: Vertex-distinguishing proper edge-colourings. J. Graph Theory 26 (2) (1997), 73-82.
• [9] Cerny J., Horńak M., Sotak R.: Observability of a graph. Math. Slovaca 46 (1996), 21-31.
• [10] Favaron O., Li H., Schelp R. H.: Strong edge colouring of graphs. Discrete Mathematics 159 (1996), 103-109.
• [11] Horńak M., Sotak R.: Observability of complete multipartite graphs with equipo-tent parts. Ars Combinatoria 41 (1995), 289-301.
• [12] Horńak M., Sotak R.: Asymptotic behaviour of the observability of Qn. Discrete Mathematics 176 (1997), 139-148.