文章基本信息

标题：On the Total Vertex Irregular Labeling of Proper Interval Graphs
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作者：A. Rana
期刊名称：Journal of Scientific Research
印刷版ISSN：2070-0237
电子版ISSN：2070-0245
出版年度：2020
卷号：12
期号：4
页码：537-543
DOI：10.3329/jsr.v12i4.45923
出版社：Rajshahi University
摘要：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.
关键词：Design of algorithms; Interval graphs; Vertex irregular total labelling; Total vertex irregularity strength.