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- W3033392632 abstract "Following Estrada [The Structure of Complex Networks, Oxford University Press, Oxford, UK, 2011], we use the word network interchangeably with in this paper. Several classes of particular nonregular graphs have been introduced in literature; for example, the classes of n-vertex connected antiregular graphs, highly irregular graphs, totally segregated graphs, maximally irregular graphs and connected stepwise irregular graphs. We denote these classes by $mathcal{A}{mathcal{R}_n}$, $mathcal{H}mathcal{I}{mathcal{R}_n}$, $mathcal{T}{mathcal{S}_n}$, $mathcal{M}mathcal{I}{mathcal{R}_n}$, $mathcal{S}mathcal{I}{mathcal{R}_n}$, respectively. The main purpose of the present study is to identify the graph classes $mathcal{A},mathcal{B} in left{ {mathcal{A}{mathcal{R}_n},mathcal{H}mathcal{I}{mathcal{R}_n},mathcal{T}{mathcal{S}_n},mathcal{M}mathcal{I}{mathcal{R}_n},mathcal{S}mathcal{I}{mathcal{R}_n}} right}$, for which one of the following properties holds: (i) $mathcal{A} cap mathcal{B} = emptyset $ (ii) $mathcal{A} subset mathcal{B}$ (iii) $mathcal{B} subset mathcal{A}$, where $mathcal{A} ne mathcal{B}$. Additionally, a new class of certain nonregular graphs, containing the class of the highly irregular graphs as a subclass, is proposed. We refer these new type of nonregular graphs as the almost highly irregular graphs and report their basic properties." @default.
- W3033392632 created "2020-06-12" @default.
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- W3033392632 date "2019-04-01" @default.
- W3033392632 modified "2023-09-25" @default.
- W3033392632 title "On the comparative study of nonregular networks" @default.
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- W3033392632 doi "https://doi.org/10.1109/ines46365.2019.9109525" @default.
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