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11.
The Randi? index R(G) of a (chemical) graph G is also called connectivity index. Hansen and Mélot [Variable neighborhood search for extremal graphs 6: analyzing bounds for the connectivity index, J. Chem. Inf. Comput. Sci. 43 (2003) 1-14] in their paper, characterized the chemical trees of given order and number of pendent vertices which have the minimum and maximum Randi? index, respectively. In this note, we point out the mistakes in the proofs of their results Theorems 8 and 10, while we still believe that the two theorems are true, and then we give their corrected proofs. 相似文献
12.
TAN Shang-wang GUO Ji-ming QI JianDepartment of Applied Mathematics Petroleum University Dongying China 《数学季刊》2004,19(1):57-62
Let T denote a tree with the diameter d(d≥2) and order n. Let P^*d,r,n-d-1denote the tree obtained by identifying the rth vertex of path Pd l and the center of starKl,K1,n-d-1, where r = r(d) is the integer part about d 2/2. Then p(T)≤ p(P^*d,r,n-d-1), andequality holds if and only if T≌P^*d,r,n-d-1 相似文献
13.
We study computable trees with distinguished initial subtree (briefly, I-trees). It is proved that all I-trees of infinite height are computably categorical, and moreover, they all have effectively infinite computable dimension. 相似文献
14.
A central problem that arises in evolutionary biology is that of displaying partitions of subsets of a finite set X on a tree whose vertices are partially labelled with the elements of X. Such a tree is called an X-tree and, for a collection of partitions of subsets of X, characterisations for the existence and uniqueness of an X-tree that displays have been previously given in terms of chordal graphs. In this paper, we obtain two closely related characterisations also in terms of chordal graphs. The first describes when identifies an X-tree, and the second describes when a compatible subset of is of maximum size. 相似文献
15.
本在Glover—Klingman算法及最小费用支撑树对策的基础上,讨论了最小费用k度限制树对策问题.利用威胁、旁支付理论制订了两种规则,并利用优超、策略等价理论分别给出了在这两种规则下最小费用k度限制树对策核心中的解,从而证明了在这两种规则下其核心非空. 相似文献
16.
The authors consider the limiting behavior of various branches in a uniform recursive tree with size growing to infinity.The limiting distribution ofζ_(n,m),the number of branches with size m in a uniform recursive tree of order n,converges weakly to a Poisson distribution with parameter 1/m with convergence of all moments.The size of any large branch tends to infinity almost surely. 相似文献
17.
Asiswellknown,thetheoryfornonlinearpolymerizationswasinitiatedbyFloryandStockmayer[1—3].MillerandMacosko[4—6]proposedarecursivemethodfordealingwiththeproblemofthepostgelpropertiesofthenetworkformingpolymerization.Stepto[7]investigatedthegelgelreactionofRAft… 相似文献
18.
The lattice model for equilibrium polymerization in a solvent proposed by Wheeler and Pfeuty is solved exactly on a Bethe lattice (core of a Caylay tree) with general coordination numberq. Earlier mean-field results are reobtained in the limitq, but the phase diagrams show deviations from them for finiteq. Whenq=2, our results turn into the solution of the one-dimensional problem. Although the model is solved directly, without the use of the correspondence between the equilibrium polymerization model and the diluten0 model, we verified that the latter model may also be solved on the Bethe lattice, its solution being identical to the direct solution in all parameter space. As observed in earlier studies of the puren0 vector model, the free energy is not always convex. We obtain the region of negative susceptibility for our solution and compare this result with mean field and renormalization group (-expansion) calculations. 相似文献
19.
The Randić index of an organic molecule whose molecular graph is G is the sum of the weights (d(u)d(v))−1/2 of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G. We give a sharp lower bound on the Randić index of conjugated trees (trees with a perfect matching) in terms of the number
of vertices. A sharp lower bound on the Randić index of trees with a given size of matching is also given
Mei Lu: Partially supported by NNSFC (No. 60172005)
Lian-zhu Zhang: Partially supported by NNSFC (No. 10271105)
Feng Tian: Partially supported by NNSFC (No. 10431020) 相似文献
20.