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## Discussiones Mathematicae Graph Theory

2015 | 35 | 2 | 301-311
Tytuł artykułu

### Characterizing which Powers of Hypercubes and Folded Hyper- cubes Are Divisor Graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we show that Qkn is a divisor graph, for n = 2, 3. For n ≥ 4, we show that Qkn is a divisor graph iff k ≥ n − 1. For folded-hypercube, we get FQn is a divisor graph when n is odd. But, if n ≥ 4 is even integer, then FQn is not a divisor graph. For n ≥ 5, we show that (FQn)k is not a divisor graph, where 2 ≤ k ≤ [n/2] − 1.
Słowa kluczowe
EN
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
301-311
Opis fizyczny
Daty
wydano
2015-05-01
otrzymano
2014-01-16
poprawiono
2014-07-22
zaakceptowano
2014-07-22
online
2015-04-18
Twórcy
autor
• Department of Basic Sciences Al-Zarka University College Al-Balqa’ Applied University Zarqa 313, Jordan, emanhijleh@bau.edu.jo
autor
• Departments of Mathematics Faculty of Science The University of Jordan Amman 11942, Jordan, o.abughneim@ju.edu.jo
autor
• Departments of Mathematics Faculty of Science The University of Jordan Amman 11942, Jordan, alezehh@ju.edu.jo
Bibliografia
• [1] E.A. AbuHijleh, O.A. AbuGhneim and H. Al-Ezeh, Characterizing when powers of a caterpillar are divisor graphs, Ars Combin. 113 (2014) 85-95.
• [2] S. Aladdasi, O.A. AbuGhneim and H. Al-Ezeh, Divisor orientations of powers of paths and powers of cycles, Ars Combin. 94 (2010) 371-380.
• [3] S. Aladdasi, O.A. AbuGhneim and H. Al-Ezeh, Characterizing powers of cycles that are divisor graphs, Ars Combin. 97 (2010) 447-451.
• [4] S. Al-Addasi, O.A. AbuGhneim and H. Al-Ezeh, Merger and vertex splitting in divisor graphs, Int. Math. Forum 5 (2010) 1861-1869.
• [5] S. Aladdasi, O.A. AbuGhneim and H. Al-Ezeh, Further new properties of divisor graphs, J. Combin. Math. Combin. Comput. 81 (2012) 261-272.
• [6] G. Agnarsson, R. Greenlaw, Graph Theory: Modeling Applications and Algorithms (Pearson, NJ, USA, 2007).
• [7] G. Chartrand, R. Muntean, V. Seanpholphat and P. Zang, Which graphs are divisor graphs, Congr. Numer. 151 (2001) 180-200.
• [8] P. Erdős, R. Frued and N. Hegyvári, Arithmetical properties of permutations of integers, Acta Math. Hungar. 41 (1983) 169-176. doi:10.1007/BF01994075[Crossref]
• [9] S.Y. Hsieh, C.N. Kuo, Hamiltonian-connectivity and strongly Hamiltonian-laceability of folded hypercubes, Comput. Math. Appl. 53 (2006) 1040-1044. doi:10.1016/j.camwa.2006.10.033[WoS][Crossref]
• [10] M. Kobeissi, M. Mollard, Disjoint cycles and spanning graphs of hypercubes, Discrete Math. 288 (2004) 73-87. doi:10.1016/j.disc.2004.08.005[Crossref]
• [11] O. Melnikov, V. Sarvanov, R. Tyshkevich, V. Yemelichev and I. Zverovich, Exercises in Graph Theory (Netherlands, Kluwer Academic Publishers, 1998). doi:10.1007/978-94-017-1514-0[Crossref]
• [12] A.D. Pollington, There is a long path in the divisor graph, Ars Combin. 16-B (1983) 303-304.
• [13] C. Pomerance, On the longest simple path in the divisor graph, Congr. Numer. 40 (1983) 291-304.
• [14] G.S. Singh, G. Santhosh, Divisor graph-I, preprint.
Typ dokumentu
Bibliografia
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