To solve the access-balancing problem in distributed storage systems, we introduce a new combinatorial model, called MinVar model for fractional repetition (FR) codes. Since FR codes are based on graphs or set our is characterized by property that variance among sums of block-labels incident to fixed vertex minimized. This characterization different from Dau and Milenkovic's MaxMinSum while min...

BaEa, M., On magic labelings of honeycomb, Discrete Mathematics 105 (1992) 305-311. We deal with the problem of labeling the vertices, edges and faces of a hexagonal planar map in such a way that the label of a face and labels of vertices and edges surrounding that face add up to a fixed value.

A graph labeling is an assignment of integers to the vertices, or edges, or both subject to certain conditions. In this paper, we prove the existence of Z3magic, and Z4bi magic labelings for the middle graph of extended duplicate graph of a path by presenting algorithms.