On Distance Irregularity Strength of Lollipop, Centipede, and Tadpole Graphs

Kusbudiono, C.H. Pratiwi, Kristiana Wijaya

2018

Abstract

Let G be a simple graph. A distance irregular vertex k-labelling of a graph G is defined as a labelling λ:V(G)⟶{1,2,…,k} which is every two distinct vertices x,y∈V(G) have different weights, wt(x)≠wt(y). The weight of a vertex x in G, denoted by wt(x), is the sum of the labels of all the vertices adjacent to x (distance 1 from x), namely, wt(x)= ∑y∈N(x)λ(y), where N(x) is the set of all the vertices adjacent to x. The minimum k for which the graph G has a distance irregular vertex k-labelling is called the distance irregularity strength of G and denoted by dis(G). In this paper, we determine the exact value of the distance irregularity strength of lollipop, tadpole, and centipede graphs.

Paper Citation

in Harvard Style

Kusbudiono., Pratiwi C. and Wijaya K. (2018). On Distance Irregularity Strength of Lollipop, Centipede, and Tadpole Graphs.In Proceedings of the International Conference on Mathematics and Islam - Volume 1: ICMIs, ISBN 978-989-758-407-7, pages 233-235. DOI: 10.5220/0008519902330235

in Bibtex Style

@conference{icmis18,
author={Kusbudiono and C.H. Pratiwi and Kristiana Wijaya},
title={On Distance Irregularity Strength of Lollipop, Centipede, and Tadpole Graphs},
booktitle={Proceedings of the International Conference on Mathematics and Islam - Volume 1: ICMIs,},
year={2018},
pages={233-235},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0008519902330235},
isbn={978-989-758-407-7},
}

in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Mathematics and Islam - Volume 1: ICMIs,
TI - On Distance Irregularity Strength of Lollipop, Centipede, and Tadpole Graphs
SN - 978-989-758-407-7
AU - Kusbudiono.
AU - Pratiwi C.
AU - Wijaya K.
PY - 2018
SP - 233
EP - 235
DO - 10.5220/0008519902330235