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.


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.


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

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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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