Highly irregular graphs with extreme numbers of edges

Majcher, Zofia; Michael, Jerzy

doi:10.1016/s0012-365x(96)00056-8

Cited by 21 publications

(10 citation statements)

References 2 publications

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“…Paul Erdos emphasized this in the study of irregular graphs for the first time in history in [25]. In the Second Krakow Conference on Graph eory, Erdos officially posed an open problem to " determine the extreme size of highly irregular graphs of given order" [26][27][28]. Since then, irregular graphs and the degree of irregularity have become one of the core open problems of graph theory.…”

Section: Preliminaries and Notationsmentioning

confidence: 99%

Molecular Irregularity Indices of Nanostar, Fullerene, and Polymer Dendrimers

Quan

Wang

Munir

et al. 2020

Journal of Chemistry

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Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. Some properties like toxicity, entropy, and heats of vaporization of these dendrimers can be forecasted using topological indices. e present article is devoted to study of irregularity indices of three well-known classes of dendrimers, namely, nanostar dendrimer D [p], fullerene dendrimer NS 4 [p], and polymer dendrimerNS 5 [p], where p is the step size. We also see the relation of irregularity of these dendrimers on the step size graphically.

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Section: Preliminaries and Notationsmentioning

confidence: 99%

Molecular Irregularity Indices of Nanostar, Fullerene, and Polymer Dendrimers

Quan

Wang

Munir

et al. 2020

Journal of Chemistry

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“…Paul Erdos emphasized the study of irregular graphs for the first time in history in [22]. At the Second Krakow Conference on Graph Theory (1994), Erdos officially posed an open problem about determination of the extreme size of highly irregular graphs of given order [23]. Since then, the irregular graphs and the degree of irregularity have become the basic open problem of graph theory.…”

Section: Preliminaries and Notationsmentioning

confidence: 99%

Imbalance-Based Irregularity Molecular Descriptors of Nanostar Dendrimers

et al. 2019

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Dendrimers are branched organic macromolecules with successive layers of branch units surrounding a central core. The molecular topology and the irregularity of their structure plays a central role in determining structural properties like enthalpy and entropy. Irregularity indices which are based on the imbalance of edges are determined for the molecular graphs associated with some general classes of dendrimers. We also provide graphical analysis of these indices for the above said classes of dendrimers.

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“…This concept was, in an implicit manner, used in the early works [5,6,39,40], but was explicitly considered only quite recently [36,37,41,42].…”

Section: Irregularity Indexmentioning

confidence: 99%

“…Such "opposite" graphs should be highly irregular. During the Second Krakow Conference on Graph Theory (1994), Erdős officially posed as an open problem the determination of the extreme size of highly irregular graphs of given order [40].…”

Section: Introductionmentioning

confidence: 99%