The Second Minimum of the Irregularity of Graphs

Nasiri, Ramin; Fath-Tabar, Gholam Hossein

doi:10.1016/j.endm.2013.11.026

Cited by 11 publications

(7 citation statements)

References 2 publications

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“…Fath-Tabar [25] set up some new bounds on the Zagreb indices using the irregularity of graphs. Furthermore, Nasiri et al [26,27], determined the second minimum of the irregularity and total irregularity indices in all graphs. Some new spectral bounds for graph irregularity have been given in [28].…”

Section: Introductionmentioning

confidence: 99%

On Irregularity Measures of Some Dendrimers Structures

et al. 2019

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A graph is said to be a regular graph if all its vertices have the same degree, otherwise, it is irregular. Irregularity indices are usually used for quantitative characterization of the topological structure of non-regular graphs. In numerous applications and problems in material engineering and chemistry, it is useful to be aware that how irregular a molecular structure is? Furthermore, evaluations of the irregularity of underline molecular graphs could be valuable for QSAR/QSPR studies, and for the expressive determines of chemical and physical properties, such as enthalpy of vaporization, toxicity, resistance, Entropy, melting and boiling points. In this paper, we think over the following four irregularity measures: the irregularity index by Albertson, σ irregularity index, the total irregularity index and the variance of vertex degrees. By way of graph structural estimation and derivations, we determine these irregularity measures of the molecular graphs of different classes of dendrimers.

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Section: Introductionmentioning

confidence: 99%

On Irregularity Measures of Some Dendrimers Structures

et al. 2019

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“…With the passage of time, the idea of understanding compounds through TIs gained significant importance in the field of medicine because it does not require chemical-related apparatus to study [2]. TIs are being intensively studied for different graphs, especially for chemical graphs, for example, see [3][4][5][6]. TIs can be separated into various classes, specifically distance-based indices, degree-based indices, eigenvalue-based indices, and mixed indices.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Irregularity Indices of Several Dendrimers Structures

et al. 2019

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Irregularity indices are usually used for quantitative characterization of the topological structures of non-regular graphs. In numerous problems and applications, especially in the fields of chemistry and material engineering, it is useful to be aware of the irregularity of a molecular structure. Furthermore, the evaluation of the irregularity of graphs is valuable not only for quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies but also for various physical and chemical properties, including entropy, enthalpy of vaporization, melting and boiling points, resistance, and toxicity. In this paper, we will restrict our attention to the computation and comparison of the irregularity measures of different classes of dendrimers. The four irregularity indices which we are going to investigate are σ irregularity index, the irregularity index by Albertson, the variance of vertex degrees, and the total irregularity index.

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“…Gao et al [7] discuss acyclic, unicyclic, and bicyclic graphs and find sharp bounds for their Hyper-Zagreb index. The degree of vertices is the main part of some other graph invariants such as irregularity and total irregularity, see [6,[16][17][18]. To become more familiar with this topic, one should go through related literature including [2,5,15,21].…”

Section: Introductionmentioning

confidence: 99%