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2021•Open Journal of Discrete MathematicsOpen access

A Note on n-Set Distance-Labelings of Graphs

Roger K. Yeh

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Abstract

This note is considered as a sequel of Yeh [1]. Here, we present a generalized (vertex) distance labeling (labeling vertices under constraints depending the on distance between vertices) of a graph. Instead of assigning a number (label) to each vertex, we assign a set of numbers to each vertex under given conditions. Some basic results are given in the first part of the note. Then we study a particular class of this type of labelings on several classes of graphs.

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What this paper is about

This note is considered as a sequel of Yeh [1]. Here, we present a generalized (vertex) distance labeling (labeling vertices under constraints depending the on distance between vertices) of a graph. Instead of assigning a number (label) to each vertex, we assign a set of numbers to each vertex under given conditions. Some basic results are given in the first part of the note. Then we study a particular class of this type of labelings on several classes of graphs.

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Available abstract

This note is considered as a sequel of Yeh [1]. Here, we present a generalized (vertex) distance labeling (labeling vertices under constraints depending the on distance between vertices) of a graph. Instead of assigning a number (label) to each vertex, we assign a set of numbers to each vertex under given conditions. Some basic results are given in the first part of the note. Then we study a particular class of this type of labelings on several classes of graphs.

Key concepts: Combinatorics, Vertex (graph theory), Mathematics, Edge-graceful labeling, Graph, Vertex connectivity, Discrete mathematics, Line graph

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