All 2-regular graphs consisting of 4-cycles are graceful

Abrham, Jaromir; Kotzig, Anton

doi:10.1016/0012-365x(93)e0095-l

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2016

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Cited by 9 publications

(3 citation statements)

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“…In these tables, the symbols 'α' and 'β' denote that two and four cycles are fixed respectively. The integer programming model for 3C4 , or (1,3), shows that there is no feasible labeling for this graph in less than 1 second. Also, the tabu search algorithm shows that no feasible solution for this problem exists in a reasonable amount of time.…”

Section: Computational Resultsmentioning

confidence: 99%

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An Integer Programming Model and a Tabu Search Algorithm to Generate α-labeling of Special Classes of Quadratic Graphs

Eshghi

Salarrezaei

2016

IJOR

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First, an integer programming model is proposed to find an α-labeling for quadratic graphs (, 4). Then, a Tabu search algorithm is developed to solve large scale problems. The proposed approach can generate α-labeling for special classes of quadratic graphs (, 4), 6 ≤ ≤ 10, 2 ≤ ≤ 10, not previously reported in the literature. Then, the main theorem of the paper is presented. We show how a problem in graph theory can be modeled and solved by an integer programming model and a metaheuristic approach.

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Section: Computational Resultsmentioning

confidence: 99%

“…-For > 0 and ≠ 3, graph ( , 1) has an -labeling. Graph (3,1) is graceful but does not have an -labeling [1]. -For ≥ 2, (3,4 ) has an -labeling [13].…”

Section: Introductionmentioning

confidence: 99%