On the Total Vertex Irregular Labeling of Proper Interval Graphs

Authors

  • A. Rana Department of Mathematics, Narajole Raj College, Paschim Medinipur, West Bengal, 721211, India

DOI:

https://doi.org/10.3329/jsr.v12i4.45923

Abstract

A labeling of a graph is a mapping that maps some set of graph elements to a set of numbers (usually positive integers).  For a simple graph G = (V, E) with vertex set V and edge set E, a labeling  Φ: V ∪ E → {1, 2, ..., k} is called total k-labeling. The associated vertex weight of a vertex x∈ V under a total k-labeling  Φ is defined as wt(x) = Φ(x) + y∈N(x) Φ(xy) where N(x) is the set of neighbors of the vertex x. A total k-labeling is defined to be a vertex irregular total labeling of a graph, if for every two different vertices x and y of G, wt(x)≠wt(y). The minimum k for which  a graph G has a vertex irregular total k-labeling is called the total vertex irregularity strength of G, tvs(G). In this paper, total vertex irregularity strength of interval graphs is studied. In particular, an efficient algorithm is designed to compute tvs of proper interval graphs and bounds of tvs is presented for interval graphs.

Downloads

Download data is not yet available.
Abstract
317
pdf
332

Downloads

Published

2020-09-01

How to Cite

Rana, A. (2020). On the Total Vertex Irregular Labeling of Proper Interval Graphs. Journal of Scientific Research, 12(4), 537–543. https://doi.org/10.3329/jsr.v12i4.45923

Issue

Section

Section A: Physical and Mathematical Sciences