Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Notion of Valued Set

Version 1 : Received: 18 July 2021 / Approved: 19 July 2021 / Online: 19 July 2021 (12:41:02 CEST)

How to cite: Garrett, H. Notion of Valued Set. Preprints 2021, 2021070410 (doi: 10.20944/preprints202107.0410.v1). Garrett, H. Notion of Valued Set. Preprints 2021, 2021070410 (doi: 10.20944/preprints202107.0410.v1).

Abstract

The aim of this article is to introduce the new notion on a given graph. The notions of valued set, valued function, valued graph and valued quotient are introduced. The attributes of these new notions are studied. Valued set is about the set of vertices which have the maximum number of neighbors. The kind of partition of the vertex set to the vertices of the valued set is introduced and its attributes are studied. The behaviors of classes of graphs under these new notions are studied and the algebraic operations on these sets in the different situations get new result to understand the classes of graphs, these notions and the general graphs better and more.

Keywords

Vertex’s Neighbors; Valued Set; Valued Function; Valued Quotient

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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