Displaying similar documents to “Nearly antipodal chromatic number a c ' ( P n ) of the path P n ”

A note on radio antipodal colourings of paths

Riadh Khennoufa, Olivier Togni (2005)

Mathematica Bohemica

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The radio antipodal number of a graph G is the smallest integer c such that there exists an assignment f V ( G ) → { 1 , 2 , ... , c } satisfying | f ( u ) - f ( v ) | ≥ D - d ( u , v ) for every two distinct vertices u and v of G , where D is the diameter of G . In this note we determine the exact value of the antipodal number of the path, thus answering the conjecture given in [G. Chartrand, D. Erwin and P. Zhang, Math. Bohem. 127 (2002), 57–69]. We also show the connections between this colouring and radio labelings.

A note on the number of solutions of the generalized Ramanujan-Nagell equation x 2 - D = p n

Yuan-e Zhao, Tingting Wang (2012)

Czechoslovak Mathematical Journal

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Let D be a positive integer, and let p be an odd prime with p ∤ D . In this paper we use a result on the rational approximation of quadratic irrationals due to M. Bauer, M. A. Bennett: Applications of the hypergeometric method to the generalized Ramanujan-Nagell equation. Ramanujan J. 6 (2002), 209–270, give a better upper bound for N ( D , p ) , and also prove that if the equation U 2 - D V 2 = - 1 has integer solutions ( U , V ) , the least solution ( u 1 , v 1 ) of the equation u 2 - p v 2 = 1 satisfies p ∤ v 1 , and D > C ( p ) , where C ( p ) is an effectively computable...