Hamiltonian Indices of Three Classes of Graphs Obtained from Petersen Graph

In this paper, we mainly consider the Hamiltonian indices of three classes of graphs obtained from Petersen graph, that is, the minimum integer m of m-time iterated line graph Lm(G) of these three classes of graphs such that Lm(G) is Hamiltonian. We show that the Hamiltonian indices of those graphs...

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Bibliographic Details
Published in:Axioms 2023-06, Vol.12 (6), p.580
Main Authors: Lv, Shengmei, Zhao, Liying
Format: Article
Language:English
Subjects:
Graph theory
Graphs
hamiltonian index
iterated line graph
Mathematical research
petersen graph
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Summary:In this paper, we mainly consider the Hamiltonian indices of three classes of graphs obtained from Petersen graph, that is, the minimum integer m of m-time iterated line graph Lm(G) of these three classes of graphs such that Lm(G) is Hamiltonian. We show that the Hamiltonian indices of those graphs obtained by replacing every vertex of Petersen graph with a n-cycle or a complete graph of order n, or adding n pendant edges to each vertex of Petersen graph are both 2. In addition, we also study the situations of adding an edge to these three classes of graphs and obtain that their Hamiltonian indices are both 2.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12060580