| 三角系统T_n的匹配数与点独立集数 |
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| 引用本文： | 王守中,江蓉.三角系统T_n的匹配数与点独立集数[J].西南师范大学学报(自然科学版),2010,35(1). |
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| 作者姓名： | 王守中 江蓉 |
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| 作者单位： | 广东茂名学院理学院,广东,茂名,525000 |
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| 摘 要： | 给出了一类三角系统Tn的匹配数和点独立集数的一种计算方法和计算公式,证明了:定理1(a)μ(Tn)=μ(Tn-1)+μ(Tn-2)+μ(Tn-3)+μ(Tn-4)(n≥8);(b)σ(Tn)=σ(Tn-1)+σ(Tn-3)(n≥7).定理2设ri(i=1,2,3,4)为非负整数,则(a)当n≥8时,有μ(Tn)=28∑r1+2r2+3r3+4r4=n(r1+r2+r3+r4)!r1!r2!r3!r4!+26∑r1+2r2+3r3+4r4=n-1(r1+r2+r3+r4)!r1!r2!r3!r4!+23∑r1+2r2+3r3+4r4=n-2(r1+r2+r3+r4)!r1!r2!r3!r4!+15∑r1+2r2+3r3+4r4=n-3(r1+r2+r3+r4)!r1!r2!r3!r4!;(b)当n≥7时,有σ(Tn)=14∑r1+3r2=n(r1+r2)!r1!r2!+6∑r1+3r2=n-1(r1+r2)!r1!r2!+9∑r1+3r2=n-2(r1+r2)!r1!r2!
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| 关 键 词： | 三角系统 匹配数 完美匹配数 点独立集数 |
The Numbers of Matchings and Independent-sets with Respect to the Triangular Lattice T_n |
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| WANG Shou-zhong,JIANG Rong.The Numbers of Matchings and Independent-sets with Respect to the Triangular Lattice T_n[J].Journal of Southwest China Normal University(Natural Science),2010,35(1). |
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| Authors: | WANG Shou-zhong JIANG Rong |
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| Abstract: | One gives out a kind of method and formulae to calculate the numbers of matchings, the numbers of independent-sets and the numbers of perfect matchings in a triangular lattice T_n. |
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| Keywords: | triangular lattice matching-number perfect matchings-number independent-set-number |
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