@article{Article_55,

title = {The generalized Randiˆc Index of Graph},

journal = {Communications in Combinatorics, Cryptography & Computer Science},

volume = {2023},

issue = {1},

issn = { 2783-5456 },

year = {2023},

url = {http://cccs.sgh.ac.ir/Articles/2023/issue 1/1-7-ThegeneralizedRandicIndexofGraph.pdf},

author = {Hossein Teimoori Faal},

keywords = {The value of an edge, The value of a clique, The clique handshaking lemma.},

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.}

};