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| Ordering Trees with Nearly Perfect Matchings by Algebraic Connectivity |
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Citation： |
Li ZHANG,Yue LIU.Ordering Trees with Nearly Perfect Matchings by Algebraic Connectivity[J].Chinese Annals of Mathematics B,2008,29(1):71~84 |
| Page view： 1160
Net amount： 784 |
Authors： |
Li ZHANG; Yue LIU |
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| Abstract： |
Let ${\cal T}2k+1$ be the set of trees on $2k+1$ vertices with nearly perfect matchings and $\alpha(T)$ be the algebraic connectivity of a tree $T$. The authors determine the largest twelve values of the algebraic connectivity of the trees in ${\cal T}2k+1$. Specifically, $10$ trees $T2,T3, \cdots, T11$ and two classes of trees $T(1)$ and $T(12)$ in ${\cal T}2k+1$ are introduced. It is shown in this paper that for each tree $T1',\ T1''\in T(1)$ and $T12',\ T12''\in T(12)$ and each $i,\ j$ with $2\leq i< j\leq 11$,$\alpha(T1')=\alpha T1'')>\alpha(Ti)>\alpha(Tj)>\alpha(T12')=\alpha(T12'')$.It is also shown that for each tree $T$ with $T\in {\cal T}2k+1\setminus (T(1)\cup \{T2, T3,\cdots, T11\}\cup T(12))$, $\alpha(T12')>\alpha(T).$ |
Keywords： |
Laplacian eigenvalue, Tree, Nearly perfect matching, Algebraic connectivity |
Classification： |
05C50 |
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