Decomposition of complete graphs into connected unicyclic graphs with eight edges and pentagon

<p>A <span class="math"><em>G</em></span>-decomposition of the complete graph <span class="math"><em>K</em><sub><em>n</em></sub></span> is a family of pairwise edge disjoint subgraphs of <span class=...

وصف كامل

التفاصيل البيبلوغرافية
الحاوية / القاعدة:Indonesian Journal of Combinatorics
المؤلفون الرئيسيون: Dalibor Froncek, O'Neill Kingston
التنسيق: مقال
اللغة:الإنجليزية
منشور في: InaCombS; Universitas Jember; dan Universitas Indonesia 2019-06-01
الموضوعات:
الوصول للمادة أونلاين:http://www.ijc.or.id/index.php/ijc/article/view/75
الوصف
الملخص:<p>A <span class="math"><em>G</em></span>-decomposition of the complete graph <span class="math"><em>K</em><sub><em>n</em></sub></span> is a family of pairwise edge disjoint subgraphs of <span class="math"><em>K</em><sub><em>n</em></sub></span>, all isomorphic to <span class="math"><em>G</em></span>, such that every edge of <span class="math"><em>K</em><sub><em>n</em></sub></span> belongs to exactly one copy of <span class="math"><em>G</em></span>. Using standard decomposition techniques based on <span class="math"><em>ρ</em></span>-labelings, introduced by Rosa in 1967, and their modifications we show that each of the ten non-isomorphic connected unicyclic graphs with eight edges containing the pentagon decomposes the complete graph <span class="math"><em>K</em><sub><em>n</em></sub></span> whenever the necessary conditions are satisfied.</p>
تدمد:2541-2205