Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Valued Number And Set

Version 1 : Received: 10 August 2021 / Approved: 10 August 2021 / Online: 10 August 2021 (10:13:13 CEST)

How to cite: Garrett, H. Valued Number And Set. Preprints 2021, 2021080229. https://doi.org/10.20944/preprints202108.0229.v1 Garrett, H. Valued Number And Set. Preprints 2021, 2021080229. https://doi.org/10.20944/preprints202108.0229.v1

## Abstract

In this essay, the new notion concerning longest path is introduced. Longest path has a close relation with the notion of diameter in graph. The classes of graph are studied in the terms of having the vertex with longest path. Valued number is the number of edges belong to the longest path in the matter of vertex. For every vertex, there’s a valued number and new notion of valued set is the generalization of valued number for the vertex when all vertices of the graphs are corresponded to a vertex which has the greater valued number. For any positive integer, there’s one graph in that, there’s vertex which its valued number is that. By deleting the vertices which don’t belong to valued set, new notion of new graph is up. It’s called valued graph. The comparison amid valued graph and initial graph is up, too.

## Keywords

Valued Number, Valued Set, Longest Path, Valued Graph

## Subject

Computer Science and Mathematics, Applied Mathematics

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