For a graph G = (V, E), a bijection f from V(G) ∪ E(G) → {1, 2, . . . , |V(G)| + |E(G)|} is called (a, d)-edge-antimagic total ((a, d)EAT) labeling of G if the edge-weights w(xy) = f(x) + f(y) + f(xy), xy ∈ E(G), form an arithmetic progression starting from a and having a common difference d, where a > 0 and d ≥ 0 are two fixed integers. An (a, d)-EAT labeling is called super (a, d)-EAT labelin...

A graph G = (V, E) is said to be magic if there exists an integer labeling f : V ∪ E −→ [1, |V ∪ E|] such that f(x) + f(y) + f(xy) is constant for all edges xy ∈ E. Enomoto, Masuda and Nakamigawa proved that there are magic graphs of order at most 3n + o(n) which contain a complete graph of order n. Bounds on Sidon sets show that the order of such a graph is at least n + o(n). We close the gap ...

objective: in recent years the use of herbal slimming supplements has increased in iran. one problem may be the illegal inclusion of synthetic drugs by some manufacturers in these products. the aim of this study is to determine four undeclared synthetic adulterants in some herbal slimming products present in the iranian market. methods: this survey studyresearched six common herbal slimming sup...

We propose a new puzzle: Label the eight vertices of cube using distinct integers between 0 and 12 (both inclusive) such that induced labeling each edge, given by sum labels its end points, causes edges to be labeled with odd numbers 1, 3, … 23. Any solution puzzle is called super odd-sum labeling. deftly discover all cube.

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...