Novel inequalities for generalized graph entropies – Graph energies and topological indices

A Note on Distance-Based Entropy of Dendrimers

“…The findings presented in this section show that the correlation between ecc and degree-ecc-entropy measures of three dendrimers is approximately R 2 ≈ 0.999, see This means that the ecc and degree-ecc-entropy measures might be interesting for further investigations in predicting the physico-chemical properties of molecules [12,14,[18][19][20][21][22][23][24]. The reasons for choosing these molecular descriptors is that the dendrimers are hyper-branched molecules the degree and eccentricity of vertices of which are important.…”

“…A number of measures using Shannon's entropy function have been introduced and investigated since the 1950s; see [5][6][7][8][9][10][11][12][13][14][15]. The discrete form of this well-known function is defined for a probability vector p = (p 1 , p 2 , .…”

On Laplacian energy in terms of graph invariants

“…It is worth noting that LE found applications not only in theoretical organic chemistry (see, e.g., [16,24,29]), but also in image processing [32] and information theory [21]. At this point it is worth mentioning that in addition to the Laplacian energy, a number of other "graph energies" have been considered.…”

Extremality of Graph Entropy Based on Degrees of Uniform Hypergraphs with Few Edges

“…Of course, different probability distributions defined on graphs contribute to different graph entropies. Up until now, a lots of graph entropies have been proposed (see [2,4,5,9,10,12,[14][15][16][17][18]20,22]). For more results on the theory and applications of the graph entropy, we refer the reader to four survey papers [5,13,19,20].…”