Non-self-centrality number of some molecular graphs

Rashid Farooq; Laiba Mudusar; Rashid Farooq; Laiba Mudusar

doi:10.3934/math.2021483

AIMS Mathematics

2021, Volume 6, Issue 8: 8342-8351. doi: 10.3934/math.2021483

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Research article

Non-self-centrality number of some molecular graphs

Rashid Farooq ^,,
Laiba Mudusar

School of Natural Sciences, National University of Sciences and Technology, H-12, Islamabad, Pakistan

Received: 08 January 2021 Accepted: 19 April 2021 Published: 31 May 2021
MSC : 05C12

Let $ \mathscr{G} $ be a molecular graph, the eccentricity $ e(w) $ of the vertex $ w $ in $ \mathscr{G} $ is the maximum distance of $ w $ from any other vertex of $ \mathscr{G} $. The non-self-centrality number (NSC) of a graph $ \mathscr{G} $ is defined by $ N(\mathscr{G}) = \sum_{w\not = z}|e(w)-e(z)|, $ where summation goes over all the unordered pairs of vertices of $ \mathscr{G} $. We determine non-self-centrality number of $ TUC_{4}C_{8} $ and $ V $-phenylenic nanotubes in this paper.
- non-self-centrality number,
- topological indices,
- eccentricity,
- molecular graphs,
- non-self-centered graphs,
- NSC number
Citation: Rashid Farooq, Laiba Mudusar. Non-self-centrality number of some molecular graphs[J]. AIMS Mathematics, 2021, 6(8): 8342-8351. doi: 10.3934/math.2021483

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Abstract

Let $ \mathscr{G} $ be a molecular graph, the eccentricity $ e(w) $ of the vertex $ w $ in $ \mathscr{G} $ is the maximum distance of $ w $ from any other vertex of $ \mathscr{G} $. The non-self-centrality number (NSC) of a graph $ \mathscr{G} $ is defined by $ N(\mathscr{G}) = \sum_{w\not = z}|e(w)-e(z)|, $ where summation goes over all the unordered pairs of vertices of $ \mathscr{G} $. We determine non-self-centrality number of $ TUC_{4}C_{8} $ and $ V $-phenylenic nanotubes in this paper.

References

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