Graphs induced by Gray codes

Wilmer, Elizabeth; Ernst, M.

doi:10.1016/s0012-365x(02)00516-2

Cited by 9 publications

(11 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Furthermore, we showed that for every n = 3 an n-bit Gray code exists which induces the complete graph K n , and hence we solved Problem 1.3 of Wilmer and Ernst in [11].…”

Section: Discussionmentioning

confidence: 94%

“…As remarked in [11], the largest Gray code known to induce a complete graph is a Gray code of length 8 appearing in [10]. With respect to complete graphs induced by Gray codes, Wilmer and Ernst in [11] posed the following problem.…”

Section: Corollary 12 the Complete Graph K N Is Gray Connectedmentioning

confidence: 99%

“…With respect to complete graphs induced by Gray codes, Wilmer and Ernst in [11] posed the following problem. In this note we shall mainly deal with Problem 1.3.…”

Section: Corollary 12 the Complete Graph K N Is Gray Connectedmentioning

confidence: 99%

See 2 more Smart Citations

A construction of Gray codes inducing complete graphs

Suparta

Zanten

2008

Discrete Mathematics

View full text Add to dashboard Cite

“…Furthermore, we showed that for every n = 3 an n-bit Gray code exists which induces the complete graph K n , and hence we solved Problem 1.3 of Wilmer and Ernst in [11].…”

Section: Discussionmentioning

confidence: 94%

Section: Corollary 12 the Complete Graph K N Is Gray Connectedmentioning

confidence: 99%

See 1 more Smart Citation

A construction of Gray codes inducing complete graphs

Suparta

Zanten

2008

Discrete Mathematics

View full text Add to dashboard Cite

“…Besides introducing some graphs G which are G-codes, Wilmer and Ernst in [14] also introduced some graphs which are induced by Gray codes. They in [14] also proposed to put attention to graphs of many edges: should not typical Gray codes induce many edges graphs?…”

Section: Introductionmentioning

confidence: 99%

“…They in [14] also proposed to put attention to graphs of many edges: should not typical Gray codes induce many edges graphs? Based on this suggestion, Suparta and van Zanten in [12] proved the existence of Gray codes inducing complete graphs.…”

Section: Introductionmentioning

confidence: 99%

Some classes of bipartite graphs induced by Gray codes

Suparta

2017

ejgta

View full text Add to dashboard Cite

A Gray code of length n is a list of all binary words of length n such that each two successive codewords differ in only one bit position. If the first and the last codewords also share this property, the Gray code is called cyclic, otherwise it is called non-cyclic. The numbers indicating bit positions in where two successive codewords differ in the list of Gray codes are called transition numbers, and the sequence of these all numbers is called the transition sequence of the Gray code. In this article, bit positions of a Gray code of length n will be counted from 1 up until n. If a graph with vertex set {1, 2, ..., n} having the property that two vertices i and j are adjacent in the graph if and only if, i and j are consecutive transitions in the transition sequence of a Gray code, then the graph is called induced by the Gray code. Some classes of bipartite graphs are shown to be induced by Gray codes. Particularly, we show that complete bipartite graphs are induced by Gray codes.

show abstract