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Some necessary and sufficient conditions for diophantine graphs
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A graph G of order n is called Diophantine if there exists a labeling function f of vertices such that gcd(f(u),f(v)) divides n for every pair adjacent vertices u,v in G. This paper defines, studies and generalizes maximal Diophantine graphs Dn, determining their independence number, number of full-degree vertices, and clique number. These parameters establish necessary conditions for the existence of Diophantine labelings.
Vertex Academic Press
Title: Some necessary and sufficient conditions for diophantine graphs
Description:
A graph G of order n is called Diophantine if there exists a labeling function f of vertices such that gcd(f(u),f(v)) divides n for every pair adjacent vertices u,v in G.
This paper defines, studies and generalizes maximal Diophantine graphs Dn, determining their independence number, number of full-degree vertices, and clique number.
These parameters establish necessary conditions for the existence of Diophantine labelings.
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