| Necessary and Sufficient Condition for Adjoint Uniqueness of the Graph $(\bigcup_{i{\in}A}P_i){\bigcup}(\bigcup_{j{\in}B}U_j)$ |
| Received:September 09, 2006 Revised:October 30, 2007 |
| Key Words:
adjointly unique minimum real root chromatically unique.
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| Fund Project:the National Natural Science Foundation of China (No.10761008); the Science Foundation of the State Education Ministry of China (No.205170). |
| Author Name | Affiliation | | WANG Jian Feng | Department of Mathematics and Information Science, Qinghai Normal University,Qinghai 810008, China
College of Mathematics and System Science, Xinjiang University, Xinjiang 830046, China | | HUANG Qiong Xiang | College of Mathematics and System Science, Xinjiang University, Xinjiang 830046, China | | LIU Ru Ying | Department of Mathematics and Information Science, Qinghai Normal University,Qinghai 810008, China
| | YE Cheng Fu | Department of Mathematics and Information Science, Qinghai Normal University,Qinghai 810008, China
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| Abstract: |
| For a graph $G$, let $h(G;x)=h(G)$ and $[G]_h$ denote the adjoint polynomial and the adjoint equivalence class of G, respectively. In this paper, a new application of $[G]_h$ is given. Making use of $[G]_h$, we give a necessary and suffcient condition for adjoint uniqueness of the graph $H$ such that $H\neq G$, where $H=(\bigcup_{i{\in}A}P_i){\bigcup}(\bigcup_ {j{\in}B}U_j)$, $A \subseteq A'=\{1,2,3,5\} \bigcup \{2n|n \in N, n \geq 3\}$, $B \subseteq B'= \{7,2n|n \in N, n \geq 5\}$ and $G=aP_1{\bigcup}a_0P_2{\bigcup}a_1P_3{\bigcup}a_2P_5{\bigcup}({\bigcup}_{i=3}^na_iP_{2i})$. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2008.04.019 |
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