Nearly antipodal chromatic number $ac^{\prime }(P_n)$ of the path $P_n$

Srinivasa Rao Kola; Pratima Panigrahi

A note on radio antipodal colourings of paths

Riadh Khennoufa, Olivier Togni (2005)

Mathematica Bohemica

Similarity:

The radio antipodal number of a graph $G$ is the smallest integer $c$ such that there exists an assignment $f V (G) \to {1, 2, ..., c}$ satisfying $| f (u) - f (v) | \geq D - d (u, v)$ 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

Similarity:

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...

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

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

Displaying similar documents to “Nearly antipodal chromatic number $a c^{'} (P_{n})$ of the path $P_{n}$ ”

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