Uniquely colorable Cayley graphs - Klotz, Walter (Ars mathematica contemporanea, 2017)
It is shown that the chromatic number ?$χ (G) = k$? of a uniquely colorable Cayley graph ?$G$? over a group ?$Γ$? is a divisor of ?$|Γ| = n$?. Each color class in a ?$k$?-coloring of ?$G$? is a coset of a subgroup of order ?$n/k$? of ?$Γ$?. Moreover, it is proved that ?$(k - 1)n$? is a sharp lower bound for the number of edges of a uniquely ?$k$?-colorable, noncomplete Cayley graph over an abelian group of order ?$n$?. Finally, we present constructions of uniquely colorable Cayley graphs by graph products.
Keywords: barvanje vozlišč; barvni razredi; Cayleyjevi graf; grafi