Geodesic
Achromatic Numbers for Circulant Graphs and Digraphs
Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 3, pp. 713-724

Voir la notice de l'article provenant de la source Library of Science

In this paper, we determine the achromatic and diachromatic numbers of some circulant graphs and digraphs each one with two lengths and give bounds for other circulant graphs and digraphs with two lengths. In particular, for the achromatic number we state that α (C_16q^2 + 20q + 7(1, 2)) = 8q + 5, and for the diachromatic number we state that dac( C⃗_32q^2 + 24q + 5 (1, 2)) = 8q + 3. In general, we give the lower bounds α(C_4q^2 + aq+1 (1, a)) ≥ 4q + 1 and dac( C⃗_8q^2+2(a+4)q+a+3 (1, a)) ≥ 4q + 3 when a is a non quadratic residue of ℤ_4q+1 for graphs and ℤ_4q+3 for digraphs, and the equality is attained, in both cases, for a = 3. Finally, we determine the achromatic index for circulant graphs of q^2 +q + 1 vertices when the projective cyclic plane of odd order q exists.
Keywords: circulant graphs, complete colorings, achromatic number, achromatic index 
@article{DMGT_2021_41_3_a1,
     author = {Araujo-Pardo, Gabriela and Montellano-Ballesteros, Juan Jos\'e and Olsen, Mika and Rubio-Montiel, Christian},
     title = {Achromatic {Numbers} for {Circulant} {Graphs} and {Digraphs}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {713--724},
     publisher = {mathdoc},
     volume = {41},
     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2021_41_3_a1/}
}
TY  - JOUR
AU  - Araujo-Pardo, Gabriela
AU  - Montellano-Ballesteros, Juan José
AU  - Olsen, Mika
AU  - Rubio-Montiel, Christian
TI  - Achromatic Numbers for Circulant Graphs and Digraphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2021
SP  - 713
EP  - 724
VL  - 41
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2021_41_3_a1/
LA  - en
ID  - DMGT_2021_41_3_a1
ER  - 
%0 Journal Article
%A Araujo-Pardo, Gabriela
%A Montellano-Ballesteros, Juan José
%A Olsen, Mika
%A Rubio-Montiel, Christian
%T Achromatic Numbers for Circulant Graphs and Digraphs
%J Discussiones Mathematicae. Graph Theory
%D 2021
%P 713-724
%V 41
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2021_41_3_a1/
%G en
%F DMGT_2021_41_3_a1
Araujo-Pardo, Gabriela; Montellano-Ballesteros, Juan José; Olsen, Mika; Rubio-Montiel, Christian. Achromatic Numbers for Circulant Graphs and Digraphs. Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 3, pp. 713-724. http://geodesic.mathdoc.fr/item/DMGT_2021_41_3_a1/