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

• Autorzy: Eman A. AbuHijleh , Omar A. AbuGhneim , Hasan Al-Ezeh
• 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

hypercube; folded-hypercube; divisor graph; power of a graph

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2015
• Tom: 35
• Numer: 2
• Strony: 301-311

Daty

wydano

2015-05-01

otrzymano

2014-01-16

poprawiono

2014-07-22

zaakceptowano

2014-07-22

online

2015-04-18

Twórcy

autor

Eman A. AbuHijleh

• Department of Basic Sciences Al-Zarka University College Al-Balqa’ Applied University Zarqa 313, Jordan

autor

Omar A. AbuGhneim

• Departments of Mathematics Faculty of Science The University of Jordan Amman 11942, Jordan

autor

Hasan Al-Ezeh

• Departments of Mathematics Faculty of Science The University of Jordan Amman 11942, Jordan

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.
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• [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.
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• [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.
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Identyfikatory

DOI

10.7151/dmgt.1801