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Irregularity of molecular graphs [PDF]
Kragujevac Journal of Science, 2016 A graph whose all vertices have equal degrees is said to be regular. If this is not the case, then the graph is irregular. Various measure of irregularity have been proposed. These are described and compared, with particular emphasis on molecular graphs.
Gutman Ivan
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The Maximal Total Irregularity of Bicyclic Graphs [PDF]
Journal of Applied Mathematics, 2014 In 2012, Abdo and Dimitrov defined the total irregularity of a graph G=(V,E) as irrtG=1/2∑u,v∈VdGu-dGv, where dGu denotes the vertex degree of a vertex u∈V.
Lihua You +3 more
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The irregularity of graphs under graph operations
Discussiones Mathematicae Graph Theory, 2014 The irregularity of a simple undirected graph G was defined by Albertson [5] as irr(G) = ∑uv∈E(G) |dG(u) − dG(v)|, where dG(u) denotes the degree of a vertex u ∈ V (G).
Abdo Hosam, Dimitrov Darko
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Computational measures of irregularity molecular descriptors of octahedral and icosahedral networks [PDF]
Frontiers in ChemistryIrregularity measures tend to describe the complexity of networks. Chemical graph theory is a branch of mathematical chemistry that has a significant impact on the development of the chemical sciences.
Xiujun Zhang +2 more
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Optimizing hybrid network topologies in communication networks through irregularity strength [PDF]
Scientific ReportsGraph theory has emerged as an influential tool for communication network design and analysis, especially for designing hybrid network topologies for local area networks (LANs).
Syed Aqib Abbas Naqvi +5 more
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New measures of graph irregularity
Electronic Journal of Graph Theory and Applications, 2014 In this paper, we define and compare three new measures of graph irregularity. We use these measures to tighten upper bounds for the chromatic number and the Colin de Verdiere parameter.
Clive Elphick, Pawel Wocjan
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On H-Irregularity Strength Of Graphs
Discussiones Mathematicae Graph Theory, 2017 New graph characteristic, the total H-irregularity strength of a graph, is introduced. Estimations on this parameter are obtained and for some families of graphs the precise values of this parameter are proved.
Ashraf Faraha +3 more
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Computing The Irregularity Strength of Planar Graphs [PDF]
Mathematics, 2018 The field of graph theory plays a vital role in various fields. One of the important areas in graph theory is graph labeling used in many applications such as coding theory, X-ray crystallography, radar, astronomy, circuit design, communication network ...
Hong Yang +4 more
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Two types irregular labelling on dodecahedral modified generalization graph
Heliyon, 2022 Irregular labelling on graph is a function from component of graph to non-negative natural number such that the weight of all vertices, or edges are distinct. The component of graph is a set of vertices, a set of edges, or a set of both. In this paper we
Nurdin Hinding +4 more
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Irregularity of Graphs Respecting Degree Bounds
The Electronic Journal of Combinatorics, 2023 Albertson defined the irregularity of a graph $G$ as $$irr(G)=\sum\limits_{uv\in E(G)}|d_G(u)-d_G(v)|.$$ For a graph $G$ with $n$ vertices, $m$ edges, maximum degree $\Delta$, and $d=\left\lfloor \frac{\Delta m}{\Delta n-m}\right\rfloor$, we show $$irr(G)\leq d(d+1)n+\frac{1}{\Delta}\left(\Delta^2-(2d+1)\Delta-d^2-d\right)m.$$
Rautenbach, Dieter, Werner, Florian
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