Original Research Article

Article volume = 2023 and issue = 1

Pages: 55–60

Article publication Date: January 28, 2023

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The generalized Randiˆc Index of Graph

Hossein Teimoori Faal

Department of Computer Science, Faculty of Mathematical and Computer Sciences, Allameh Tabataba’i University, Tehran, Iran.


Abstract:

In this paper, we first review the weighted-version of the handshaking lemma based on the weighted-version of the incidence matrix of a given graph G. Then, we obtain an extension of the handshaking lemma based on the new concept of the value of a clique in G. We also define a clique version of the Randiĉ index that we will call it the generalized Randiĉ index. More importantly, we obtain a generalization of the well-know upper bound for the Randiĉ index of a graph G due to Fajtlowicz. We finally conclude the paper with some disscussions about possible future works.

Keywords:

The value of an edge, The value of a clique, The clique handshaking lemma.


References:
  • [1] B. Bollobás, P. Erdos, Graphs of extremal weights, Ars Combin., 50 (1998) 225–233. 1.1
  • [2] S. Fajtlowicz, Written on the wall, a list of conjectures of Graffiti, Available from the author. 1.2, 3.1, 4, 6
  • [3] M. Randiĉ, On characterization of molecular branching, J. Am. Chem. Soc., 97 (1975), 6609–6615. 1, 1
  • [4] H. Teimoori, On clique values identities and Mantel-type theorems, Trans. Combin., 9 (2020), 139–146. 1, 5.3
  • [5] B. Wu, The weighted version of the handshaking lemma with an application, J. Inequal. Appl., 351 (2014) 1–5. 2.2, 3, 3
Cite this article as:
  • Hossein Teimoori Faal, The generalized Randiˆc Index of Graph, Communications in Combinatorics, Cryptography & Computer Science, 2023(1), PP.55–60, 2023
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