First degree-based entropy of graphs

Ghalavand, Ali; Eliasi, Mehdi

doi:10.1007/s12190-018-1168-x

Cited by 15 publications

(13 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Ghalavand et al [10] extended some known results about the minimum and maximum values of the degree-based entropy by the following theorem.…”

Section: Preliminariesmentioning

confidence: 96%

See 1 more Smart Citation

Graphs with minimum degree-based entropy

Dong,

Gadouleau,

Wan

et al. 2021

Preprint

View full text Add to dashboard Cite

The degree-based entropy of a graph is defined as the Shannon entropy based on the information functional that associates the vertices of the graph with the corresponding degrees. In this paper, we study extremal problems of finding the graphs attaining the minimum degree-based graph entropy among graphs and bipartite graphs with a given number of vertices and edges. We characterize the unique extremal graph achieving the minimum value among graphs with a given number of vertices and edges and present a lower bound for the degree-based entropy of bipartite graphs and characterize all the extremal graphs which achieve the lower bound. This implies the known result due to Cao et al. (2014) that the star attains the minimum value of the degree-based entropy among trees with a given number of vertices.

show abstract

“…Ghalavand et al [10] extended some known results about the minimum and maximum values of the degree-based entropy by the following theorem.…”

Section: Preliminariesmentioning

confidence: 96%

“…Ghalavand et al [10] applied majorization technique to extend some known results on the extremal values of the degree-based entropy of trees, unicyclic and bicyclic graphs.…”

Section: Introductionmentioning

confidence: 99%

Graphs with minimum degree-based entropy

Dong,

Gadouleau,

Wan

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…in [8]. Therefore, if we consider the extremal values of I 1 (G) of a class of graphs with given number of edges, it suffices to determine the extremal values…”

Section: Communications In Mathematical and In Computer Chemistrymentioning

confidence: 99%

A note on extremality of the first degree-based entropy

Yang¹

2021

match

View full text Add to dashboard Cite

show abstract

“…Most of the articles on the Reformulated Zagreb index discuss on the various properties of Reformulated first Zagreb index such as lower and upper bounds [20][21][22][23][24] . Many works are on the computation of the index of various compounds and of certain class of graphs 23,[25][26][27][28][29][30][31][32] . It has been mentioned that, among all the versions of the Zagreb indices, the reformulated first Zagreb index has a significant role in QSPR study 33 .…”

Section: The Reformulated Zagreb Indexmentioning

confidence: 99%

The QSPR Study of Butane derivatives: (A Mathematical Approach)

Asok

Kureethara

2018

Orient. J. Chem

View full text Add to dashboard Cite

The QSPR analysis provides a significant structural insight into the physiochemical properties of Butane derivatives. We study some physiochemical properties of fourteen Butane derivatives and develop a QSPR model using four topological indices and Butane derivatives. Here we analyze how closely the topological indices are related to the physiochemical properties of Butane derivatives. For this we compute analytically the topological indices of Butane derivatives and plot the graphs between each of these topological indices to the properties of Butane derivatives using Origin. This QSPR model exhibits a close correlation between Heavy atomic count, Complexity, Hydrogen bond acceptor count, and Surface tension of Butane derivatives with the Redefined first Zagreb index, the Redefined third Zagreb index, the Sum connectivity index and the Reformulated first Zagreb index, respectively.

show abstract

First degree-based entropy of graphs

Cited by 15 publications

References 11 publications

Graphs with minimum degree-based entropy

Graphs with minimum degree-based entropy

A note on extremality of the first degree-based entropy

The QSPR Study of Butane derivatives: (A Mathematical Approach)

Contact Info

Product

Resources

About