Distinguishing Number of the Generalized Theta Graph
Andi Pujo Rahadi, Edy Tri Baskoro, Suhadi Wido Saputro Β· Advances in computer science research Β· 2022
A generalized theta graph is a graph constructed from two distinct vertices by joining them with π (>=3) internally disjoint paths of lengths greater than one.The distinguishing number π·(πΊ) of a graph πΊ is the least integer π such that πΊ has a vertex labelling with π 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.