32 research outputs found
Distinguishing Number for some Circulant Graphs
Introduced by Albertson et al. \cite{albertson}, the distinguishing number
of a graph is the least integer such that there is a
-labeling of the vertices of that is not preserved by any nontrivial
automorphism of . Most of graphs studied in literature have 2 as a
distinguishing number value except complete, multipartite graphs or cartesian
product of complete graphs depending on . In this paper, we study circulant
graphs of order where the adjacency is defined using a symmetric subset
of , called generator. We give a construction of a family of
circulant graphs of order and we show that this class has distinct
distinguishing numbers and these lasters are not depending on