Hadwiger conjectured that every graph of chromatic number k admits a clique minor order k. Here we prove for ≤ 10, with unique k-coloring (up to the color names) The proof does not rely on Four Color Theorem.

This study investigates using the GOST encryption algorithm to enhance security within QRCode Indonesia Standard (QRIS). Given ubiquity of QR Codes in digital transactions, particularly for Micro, Small, and Medium Enterprises (MSMEs), robust measures are paramount. We evaluated algorithm’s ability secure data Code, converting code into an encrypted carrier decipherable only via a specially-equ...

in this paper we obtain a necessary and a sufficient condition for the set of ω_0-nearest points ( ω_0-farthest points) to be non-empty or a singleton set in normed linear spaces. we shall find a necessary and a sufficient condition for an uniquely remotal set to be a singleton set.