%0 Journal Article
%T 几类重图的阶为4的图对分解<br>Multidecompositions of Several Multigraphs for Graph-Pair of Order 4
%A 赵依凡
%A 杨卫华
%J Advances in Applied Mathematics
%P 1964-1970
%@ 2324-8009
%D 2023
%I Hans Publishing
%R 10.12677/AAM.2023.124201
%X 对于某个整数t ≥ 4，如果G和H是<span>K</span><sub>t</sub>的两个边不交的、非同构的、无孤立点的生成子图且满足E(G)∪E(H)=E(K<sub>t</sub>)，那么称(G,H)是阶为t的图对。Abueida和Daven得到了P<sub>m</sub>,P<sub>n</sub>，P<sub>m</sub>,C<sub>n</sub>，P<sub>m</sub>,K<sub>n</sub>，C<sub>m</sub>,C<sub>n</sub>，C<sub>m</sub>,K<sub>n</sub>，K<sub>m</sub>,K<sub>n</sub>的阶为4的图对分解存在的充要条件。作为其结果的推广，本文给出λ(<span>P</span><sub>m</sub><span>,P</span><sub>n</sub>)，<span>λ</span>(<span>P</span><sub>m</sub><span>,C</span><sub>n</sub>)，<span>λ</span>(<span>P</span><sub>m</sub><span>,K</span><sub>n</sub>)，<span>λ</span>(<span>C</span><sub>m</sub><span>,C</span><sub>n</sub>)，<span>λ</span>(<span>C</span><sub>m</sub><span>,K</span><sub>n</sub>)，<span>λ</span>(<span>K</span><sub>m</sub><span>,K</span><sub>n</sub>)，<span>λ</span>L(K<sup>n</sup>)的阶为4的图对分解存在的充要条件。<br />
For some integer t ≥ 4, if G and H are edge disjoint, non-isomorphic and non-isolated vertices span-ning subgraphs of <span>K</span><sub>t</sub> such that <span>E(G)∪E(H)=E(K</span><sub>t</sub><span>)</span> , then we say that   is a graph-pair of order t. Abueida and Daven have introduced the necessary and sufficient conditions of the exist-ence of multidecompositions of <span>P</span><sub>m</sub><span>,P</span><sub>n</sub><span>，P</span><sub>m</sub><span>,C</span><sub>n</sub><span>，P</span><sub>m</sub><span>,K</span><sub>n</sub><span>，C</span><sub>m</sub><span>,C</span><sub>n</sub><span>，C</span><sub>m</sub><span>,K</span><sub>n</sub><span>，K</span><sub>m</sub><span>,K</span><sub>n</sub> for graph- pair of order 4. As a generalization, we obtain the necessary and sufficient conditions of the exist-ence of multidecompositions of <span>λ(</span><span>P</span><sub>m</sub><span>,P</span><sub>n</sub><span>)，</span><span>λ</span><span>(</span><span>P</span><sub>m</sub><span>,C</span><sub>n</sub><span>)，</span><span>λ</span><span>(</span><span>P</span><sub>m</sub><span>,K</span><sub>n</sub><span>)，</span><span>λ</span><span>(</span><span>C</span><sub>m</sub><span>,C</span><sub>n</sub><span>)，</span><span>λ</span><span>(</span><span>C</span><sub>m</sub><span>,K</span><sub>n</sub><span>)，</span><span>λ</span><span>(</span><span>K</span><sub>m</sub><span>,K</span><sub>n</sub><span>)，</span><span>λ</span><span>L(K</span><sup>n</sup><span>)</span> for graph-pair of order 4.
%K 分解，图对，重图<br>Multidecompositon
%K Graph-Pair
%K Multigraph
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=64863