New Results on Edge Rotation Distance Graphs

Medha Itagi Huilgol; Chitra Ramprakash

doi:10.26708/ijmsc.2016.1.6.07

New Results on Edge Rotation Distance Graphs

International Journal of Mathematics and Soft Computing ◽

10.26708/ijmsc.2016.1.6.07 ◽

2016 ◽

Vol 6 (1) ◽

pp. 81

Author(s):

Medha Itagi Huilgol ◽

Chitra Ramprakash

Keyword(s):

Distance Graphs

Download Full-text

Unit Distance Graphs and Algebraic Integers

Discrete & Computational Geometry ◽

10.1007/s00454-019-00152-4 ◽

2019 ◽

Author(s):

Danylo Radchenko

Keyword(s):

Algebraic Integers ◽

Unit Distance ◽

Distance Graphs

Download Full-text

S-packing colorings of distance graphs G(Z,{2,t})

Discrete Applied Mathematics ◽

10.1016/j.dam.2021.04.001 ◽

2021 ◽

Vol 298 ◽

pp. 143-154

Author(s):

Boštjan Brešar ◽

Jasmina Ferme ◽

Karolína Kamenická

Keyword(s):

Distance Graphs

Download Full-text

Density of sets with missing differences and applications

Mathematica Slovaca ◽

10.1515/ms-2021-0006 ◽

2021 ◽

Vol 71 (3) ◽

pp. 595-614

Author(s):

Ram Krishna Pandey ◽

Neha Rai

Keyword(s):

Number Theory ◽

Asymptotic Density ◽

Theory Problem ◽

Distance Graphs ◽

Positive Integers ◽

Infinite Set

Abstract For a given set M of positive integers, a well-known problem of Motzkin asks to determine the maximal asymptotic density of M-sets, denoted by μ(M), where an M-set is a set of non-negative integers in which no two elements differ by an element in M. In 1973, Cantor and Gordon find μ(M) for |M| ≤ 2. Partial results are known in the case |M| ≥ 3 including some results in the case when M is an infinite set. Motivated by some 3 and 4-element families already discussed by Liu and Zhu in 2004, we study μ(M) for two families namely, M = {a, b,a + b, n(a + b)} and M = {a, b, b − a, n(b − a)}. For both of these families, we find some exact values and some bounds on μ(M). This number theory problem is also related to various types of coloring problems of the distance graphs generated by M. So, as an application, we also study these coloring parameters associated with these families.

Download Full-text