On clique values identities and mantel-type theorems

Document Type : Research Paper


Department of Mathematics and Computer Science, Allameh Tabatabai University, Tehran, Iran.


‎In this paper‎, ‎we first extend the weighted handshaking‎ ‎lemma‎, ‎using a generalization of the concept of the degree of vertices to the values of graphs‎. ‎This edge-version of the weighted handshaking lemma yields an immediate generalization of the‎ ‎Mantel's classical result which asks for the maximum number of edges in triangle-free graphs‎ ‎to the class of $K_{4}$-free graphs‎. ‎Then‎, ‎by defining the concept of value‎ ‎for cliques (complete subgraphs) of higher orders‎, ‎we also‎ ‎extend the classical result of Mantel for any graph $G$‎. ‎We finally conclude our paper with a discussion‎ ‎about the possible future works‎.


Main Subjects

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Volume 9, Issue 3 - Serial Number 3
September 2020
Pages 139-146
  • Receive Date: 08 October 2019
  • Revise Date: 20 May 2020
  • Accept Date: 27 May 2020
  • Published Online: 01 September 2020