A New Polynomial for Checkerboard-Colorable 4-Valent Virtual Graphs
Hamid Abchir, Khaled Qazaqzeh, and Mohammed Sabak
TL;DR
This paper introduces a new polynomial invariant for checkerboard-colorable 4-valent virtual graphs, offering a novel combinatorial approach to understanding the Kauffman-Jones polynomial for virtual links.
Contribution
It presents a new polynomial based on Euler circuit expansion that generalizes the Kauffman-Jones polynomial for a specific class of virtual graphs.
Findings
Provides a combinatorial formulation of the Kauffman-Jones polynomial.
Defines a new polynomial invariant for checkerboard-colorable 4-valent virtual graphs.
Establishes connections between graph invariants and virtual link polynomials.
Abstract
We assign a new polynomial to any checkerboard-colorable 4-valent virtual graph in terms of its Euler circuit expansion. This provides a new combinatorial formulation of the Kauffman-Jones polynomial for checkerboard-colorable virtual links.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Graph Theory Research · Graph Theory and Algorithms