Independence roots and independence fractals of certain graphs
Independence roots and independence fractals of certain graphs
复制标题
某些图的独立根和独立分形
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Yee
中科院分区：
文献类型：
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作者：
S. Alikhani;Yee
图G的独立多项式是多项式∑ikxk，其中ik表示G中基数k的独立集的个数。本文得到了路径Pn与循环Cn的独立多项式与jacobthal多项式的关系。求出jacobthal多项式的所有根。因此，族{Pn}和{Cn}的独立多项式的根在$(- inty,-frac{1}{4}]$中是实数且稠密的。我们还研究了路径、环、轮和某些树的独立分形或独立吸引子。
The independence polynomial of a graph G is the polynomial ∑ikxk, where ik denote the number of independent sets of cardinality k in G. In this paper, we obtain the relationships between the independence polynomial of path Pn and cycle Cn with Jacobsthal polynomial. We find all roots of Jacobsthal polynomial. As a consequence, the roots of independence polynomial of the family {Pn} and {Cn} are real and dense in $(-infty,-frac{1}{4}]$. Also we investigate the independence fractals or independence attractors of paths, cycles, wheels and certain trees.