Document Type

Article

Publication Date

9-12-2023

Publication Title

AKCE Internation Journal of Graphs and Combinatorics

Volume

21

Issue

1

First page number:

84

Last page number:

90

Abstract

For a nontrivial graph G, a subset labeling of G is a labeling of the vertices of G with nonempty subsets of the set [r]={1, 2, ... , r} for a positive integer r such that two vertices of G have disjoint labels if and only if the vertices are adjacent. The subset index ρ(G) of G is the minimum positive integer r for which G has such a subset labeling from the set [r]. If T is a tree of diameter d, then ρ(Pd+1) ≤ ρ(T). It is shown that there are several classes of trees T of diameter d such that ρ(T) = ρ(Pd+1) and for every pair a, b of integers with 4 ≤ a ≤ b,there is a tree T of diameter d such that ρ(Pd+1) = a and ρ(T) = b. Sharp bounds are established for the subset indices of the starlike trees Sr(K1,t) obtained by subdividing each edge of the star K1,t a total of r times. Other results and open questions are also presented on subset indices of trees.

Keywords

Subset labeling; subset index; tree

Disciplines

Dynamic Systems | Mathematics

File Format

PDF

File Size

1718 KB

Language

English

Rights

IN COPYRIGHT. For more information about this rights statement, please visit http://rightsstatements.org/vocab/InC/1.0/

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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