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| On Clique Mantel's Theorem | |
| Author(s): | Hossein Teimoori Faal * |
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Abstract: |
A complete subgraph of any simple graph G on k vertices is called a k-clique of G. In this paper, we first introduce the concept of the value of a k-clique (k>1) as an extension of the idea of the degree of a given vertex. Then, we obtain the generalized version of handshaking lemma which we call it clique handshaking lemma. The well-known classical result of Mantel states that the maximum number of edges in the class of triangle-free graphs with n vertices is equal to n2/4. Our main goal here is to find an extension of the above result for the class of Kω+1-free graphs, using the ideas of the value of cliques and the clique handshaking lemma. |
| Keywords: | Maximum Independent Set، Value Of A Clique، Handshaking Lemma، Double-Counting |
| Article Type: | Research/Original Article |
| Language: | English |
| Published: | Analytical and Numerical Solutions for Nonlinear Equations, Volume:7 Issue: 2, Winter and Spring 2022 |
| Pages: | 171 -178 |
| Full text: | PDF is available on the website. |