Super edge-graceful paths
Sylwia Cichacz, Dalibor Froncek, Wenjie Xu

TL;DR
This paper introduces the concept of super edge-graceful graphs, focusing on paths, and proves that all paths except for P2 and P4 possess this property, expanding understanding of graph labelings.
Contribution
The paper defines super edge-graceful graphs and establishes that all paths except P2 and P4 are super edge-graceful, providing new classifications in graph labeling theory.
Findings
All paths P_n except P_2 and P_4 are super edge-graceful.
Provides a characterization of super edge-graceful paths.
Expands the class of graphs known to have super edge-graceful labelings.
Abstract
A graph of order and size is called super edge-graceful if there is a bijection from to when is odd and from to when is even such that the induced vertex labeling defined by over all edges is a bijection from to when is odd and from to when is even. \indent We prove that all paths except and are super edge-graceful.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · graph theory and CDMA systems · Photochromic and Fluorescence Chemistry
