Distinguishing Number of the Generalized Theta Graph

DOI

10.2991/acsr.k.220202.005How to use a DOI?

Keywords

Distinguishing number; Partition dimension; Generalized theta graph

Abstract

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.

Copyright

© 2022 The Authors. Published by Atlantis Press International B.V.

Open Access

This is an open access article under the CC BY-NC license.

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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  -