湖南师范大学自然科学学报
湖南師範大學自然科學學報
호남사범대학자연과학학보
ACTA SCIENTIARUM NATURALIUM UNIVERSITATIS NORMALIS HUNANENSIS
2014年
6期
67-72
,共6页
双变量色多项式%减-缩边公式%Pascal矩阵
雙變量色多項式%減-縮邊公式%Pascal矩陣
쌍변량색다항식%감-축변공식%Pascal구진
two-variable chromatic polynomial%reduce-contract edge formula%Pascal matrix
对图论的一些著名的双变量色多项式进行比较研究,对Tutte, Potts, Matching和Dohmen多项式,从定义、表达式的关系以及性质进行比较。特别地,对Tutte多项式的减-缩边公式,给出严格证明;对其余3种,则补充了它们各自的减-缩边公式以及证明。同时,由这些减-缩边公式得出它们各自一些特殊图的色多项式的具体计算公式,显示了减-缩边公式在简化计算方面的应用。
對圖論的一些著名的雙變量色多項式進行比較研究,對Tutte, Potts, Matching和Dohmen多項式,從定義、錶達式的關繫以及性質進行比較。特彆地,對Tutte多項式的減-縮邊公式,給齣嚴格證明;對其餘3種,則補充瞭它們各自的減-縮邊公式以及證明。同時,由這些減-縮邊公式得齣它們各自一些特殊圖的色多項式的具體計算公式,顯示瞭減-縮邊公式在簡化計算方麵的應用。
대도론적일사저명적쌍변량색다항식진행비교연구,대Tutte, Potts, Matching화Dohmen다항식,종정의、표체식적관계이급성질진행비교。특별지,대Tutte다항식적감-축변공식,급출엄격증명;대기여3충,칙보충료타문각자적감-축변공식이급증명。동시,유저사감-축변공식득출타문각자일사특수도적색다항식적구체계산공식,현시료감-축변공식재간화계산방면적응용。
By comparing theTutte, Potts, Matching and Dohmen two-variable chromatic polynomials, the present work studied famous two-variable chromatic polynomials of graph.Their properties and the relationship be-tween those definitions are investigated.Especially, a grid proof to reduce-contract edge formula of Tutte, as well as the others reduce-contract edge formulas and proofs are presented.Moreover, we studied some concrete compute formulas of special graphs to each of them based on those reduce-contract edge formulas, and those reduce-contract edge formulas show the application in simplifying calculation.