On Clique Version of the Randic Index
Hossein Teimoori Faal

TL;DR
This paper introduces a generalized clique-based Randic index, extending classical graph invariants, and establishes an upper bound for this new measure, opening avenues for further research in graph theory.
Contribution
It presents a novel clique-based generalization of the Randic index and proves an upper bound for this new measure, expanding theoretical understanding.
Findings
Established a generalized version of the Randic index.
Proved an upper bound for the generalized Randic index.
Discussed potential directions for future research.
Abstract
In this paper, we first review the weighted-versiion of the handshaking lemma based on the idea of a weighted vertex-edge incidence matrix of a given graph . Then, we obtain a generalized version of the handshaking lemma based on the concept of the clique value. We also define a generalized version of Randic index. More importantly, we prove an upper bound for the generalized Randic index of a graph . We finally concluse the paper with some disscussions about possible future works.
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Taxonomy
TopicsGraph theory and applications · Graph Labeling and Dimension Problems · Nanocluster Synthesis and Applications
