Marcin Anholcer

Irregular labelings of circulant graphs

Abstract We investigate the irregularity strength ( s ( G ) ) and total vertex irregularity strength ( tvs ( G ) ) of circulant graphs C i n ( 1 , 2 , … , k ) and prove that tvs ( C i n ( 1 , 2 , … , k ) ) = ⌈ n + 2 k 2 k + 1 ⌉ , while s ( C i n ( 1 , 2 , … , k ) ) = ⌈ n + 2 k − 1 2 k ⌉ except if either n = 2 k + 1 or if k is odd and n ≡ 2 k + 1 ( mod 4 k ) , then s ( C i n ( 1 , 2 , … , k ) ) = ⌈ n + 2 k − 1 2 k ⌉ + 1 .

A simplified implementation of the least squares solution for pairwise comparisons matrices

This is a follow up to “Solution of the least squares method problem of pairwise comparisons matrix” by Bozóki published by this journal in 2008. Familiarity with this paper is essential and assumed. For lower inconsistency and decreased accuracy, our proposed solutions run in seconds instead of days. As such, they may be useful for researchers willing to use the least squares method instead of the geometric means method.

Group irregularity strength of connected graphs

We investigate the group irregularity strength (

Optimization of supply chain via reduction of complaints ratio

s_g(G)

Group Distance Magic Labeling of Direct Product of Graphs

sg(G)) of graphs, that is, we find the minimum value of

Deriving priorities from inconsistent PCM using network algorithms

s