Distinguishing Number of the Generalized Theta Graph
- 10.2991/acsr.k.220202.005How to use a DOI?
- Distinguishing number; Partition dimension; Generalized theta graph
A generalized theta graph is a graph constructed from two distinct vertices by joining them with l (>=3) internally disjoint paths of lengths greater than one. The distinguishing number D(G) of a graph G is the least integer d such that G has a vertex labelling with d labels that is preserved only by a trivial automorphism. The partition dimension of a graph G is the least k such that V(G) can be k-partitioned such that the representations of all vertices are distinct with respect to that partition. In this paper, we establish a relation between the distinguishing number and the partition dimension of a graph. We also determine the distinguishing number for the generalized theta graph.
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Cite this article
TY - CONF AU - Andi Pujo Rahadi AU - Edy Tri Baskoro AU - Suhadi Wido Saputro PY - 2022 DA - 2022/02/08 TI - Distinguishing Number of the Generalized Theta Graph BT - Proceedings of the International Conference on Mathematics, Geometry, Statistics, and Computation (IC-MaGeStiC 2021) PB - Atlantis Press SP - 22 EP - 25 SN - 2352-538X UR - https://doi.org/10.2991/acsr.k.220202.005 DO - 10.2991/acsr.k.220202.005 ID - Rahadi2022 ER -