TY - JOUR
ID - 11868
TI - Complete Forcing Numbers of Polyphenyl Systems
JO - Iranian Journal of Mathematical Chemistry
JA - IJMC
LA - en
SN - 2228-6489
AU - Liu, B.
AU - Bian, H.
AU - Yu, H.
AD - School of Mathematical Sciences, Xinjiang Normal University,
Urumqi, Xinjiang 830054, P. R. China
AD - Department of Mathematics, Xinjiang Normal University,
Urumqi, Xinjiang 830054, P.R.China
AD - College of Mathematics and System Sciences, Xinjiang University,
Urumqi 830046, P.R.China
Y1 - 2016
PY - 2016
VL - 7
IS - 1
SP - 39
EP - 46
KW - Complete forcing number
KW - Polyphenly system
KW - Global forcing number
DO - 10.22052/ijmc.2016.11868
N2 - 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 (see [1] and the references therein). Recently, the forcing on perfect matchings has been attracting more researchers attention. A forcing set of M is a subset of M contained in no other perfect matchings of G. A global forcing set of G, introduced by Vukiˇcevi´c et 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. [5] introduce and define a complete forcing set of G 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.
UR - https://ijmc.kashanu.ac.ir/article_11868.html
L1 - https://ijmc.kashanu.ac.ir/article_11868_5eb2b2f068c3fbac354c9f2fde2cfdd1.pdf
ER -