COMPLETE FORCING NUMBERS OF POLYPHENYL SYSTEMS

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LIU BINGJIE; BIAN HONG; YU HAIZHENG

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Journal: Iranian Journal of Mathematical Chemistry Year:2016 | Volume:7 | Issue:1 Page(s): 39-46

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Title

COMPLETE FORCING NUMBERS OF POLYPHENYL SYSTEMS

Author(s)

LIU BINGJIE | BIAN HONG | YU HAIZHENG | Issue Writer Certificate

Keywords

COMPLETE FORCING NUMBERQ2

POLYPHENYL SYSTEMQ2

GLOBAL FORCING NUMBERQ2

Abstract

The idea of “forcing” has long been used in many research fields, such as colorings, orientations, geodetics and dominating sets in graph theory, as well as Latin squares, block designs and Steiner systems in combinatorics [D. Donovan, E. S. Mahmoodian, C. Ramsay, A. P. Street, Defining sets in combinatorics: A survey, in: C. D. Wensley (Ed.), Surveys in Combinatorics, Cambridge Univ. Press, 2003, pp. 115-174]. Recently, the forcing on perfect matchings has been attracting more researchers’ attention. A forcing set of a perfect matching M of a graph G is a subset of M contained in no other perfect matchings of G. A global forcing set of G, introduced by Vukičvićet al., is a subset of E (G) on which there are distinct restrictions of any two different perfect matchings of G. Combining the above “forcing” and “global” ideas. Xu et al. in [COMPLETE FORCING NUMBERs of catacondensed benzenoid, J. Combin. Optim.29 (2015) 803-814.] introduced a complete forcing set of G defined as a subset of E (G) on which the restriction of any perfect matching M of G is a forcing set of M. The minimum cardinality of complete forcing sets is the COMPLETE FORCING NUMBER of G. In this paper, we give the explicit expressions for the COMPLETE FORCING NUMBER of several classes of POLYPHENYL SYSTEMs.

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APA: Copy

LIU, BINGJIE, BIAN, HONG, & YU, HAIZHENG. (2016). COMPLETE FORCING NUMBERS OF POLYPHENYL SYSTEMS. IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY, 7(1), 39-46. SID. https://sid.ir/paper/205533/en

Vancouver: Copy

LIU BINGJIE, BIAN HONG, YU HAIZHENG. COMPLETE FORCING NUMBERS OF POLYPHENYL SYSTEMS. IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY[Internet]. 2016;7(1):39-46. Available from: https://sid.ir/paper/205533/en

IEEE: Copy

BINGJIE LIU, HONG BIAN, and HAIZHENG YU, “COMPLETE FORCING NUMBERS OF POLYPHENYL SYSTEMS,” IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY, vol. 7, no. 1, pp. 39–46, 2016, [Online]. Available: https://sid.ir/paper/205533/en

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