The star sequence and the general first Zagreb index

The star sequence and the general first Zagreb index

For a simple graph, we introduce a notion of the star sequence and prove that the star sequence and the frequently sequences of a graph are inverses of each other from a combinatorial point of view. As a consequence, we express the general first Zagreb index in terms of the star sequence. Also, we c...

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Veröffentlicht in:arXiv.org 2017-06
Hauptverfasser: Bedratyuk, Leonid, Savenko, Oleg
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Combinatorial analysis
Graph theory
Sequences
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description For a simple graph, we introduce a notion of the star sequence and prove that the star sequence and the frequently sequences of a graph are inverses of each other from a combinatorial point of view. As a consequence, we express the general first Zagreb index in terms of the star sequence. Also, we calculate the ordinary generating function and find a linear recurrence relation for the sequence of the general first Zagreb indexes.
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subjects Combinatorial analysis
Graph theory
Sequences
title The star sequence and the general first Zagreb index
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