| On the Minimum Real Roots of the Adjoint Polynomials of Graphs |
| Received:September 18, 2006 Revised:September 04, 2007 |
| Key Words:
chromatic polynomial adjoint polynomial roots.
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| Fund Project:the National Natural Science Foundation of China (Nos.10461009; 10641003); the Key Project of Chinese Ministry of Education (No.206158). |
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| Abstract: |
| In this paper, we are concerned with the minimum real root of the adjoint polynomial of the connected graph $G$ with cut-vertex $u$, in which $G-u$ contains paths, circles or $D_{n}$ components. Here $D_{n}$ is the graph obtained from $K_{3}$ and path $P_{n-2}$ by identifying a vertex of $K_{3}$ with an end-vertex of $P_{n-2}$. Some relevant ordering relations are obtained. This extends several previous results on the minimum roots of the adjoint polynomials of graphs. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2008.04.032 |
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