- Tytuł:
- Achromatic Numbers for Circulant Graphs and Digraphs
- Autorzy:
-
Araujo-Pardo, Gabriela
Montellano-Ballesteros, Juan José
Olsen, Mika
Rubio-Montiel, Christian - Powiązania:
- https://bibliotekanauki.pl/articles/32222712.pdf
- Data publikacji:
- 2021-08-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
circulant graphs
complete colorings
achromatic number
achromatic index - Opis:
- 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 $ \alpha (C_{16q^2 + 20q + 7}(1, 2)) = 8q + 5 $, and for the diachromatic number we state that $ dac( \vec{C}_{32q^2 + 24q + 5} (1, 2)) = 8q + 3$. In general, we give the lower bounds $ \alpha(C_{4q^2 + aq+1} (1, a)) \ge 4q + 1$ and $ dac( \vec{C}_{8q^2+2(a+4)q+a+3} (1, a)) \ge 4q + 3 $ when $a$ is a non quadratic residue of $\mathbb{Z}_{4q+1} $ for graphs and $ \mathbb{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.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2021, 41, 3; 713-724
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł