Hamiltonian Indices of Three Classes of Graphs Obtained from Petersen Graph

Author:

Lv Shengmei1ORCID,Zhao Liying1

Affiliation:

1. Department of Mathematics and Statistics, Qinghai Minzu University, Xining 810007, China

Abstract

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.

Funder

2023 Qinghai Minzu University Fund

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Reference17 articles.

1. Bondy, J.A., and Murty, U.S.R. (1976). Graph Theory with Applications, Elsevier.

2. On eulerian and hamiltonian graphs and line graphs;Harary;Canad. Math. Bull.,1965

3. On hamiltonian line-graphs;Chartrand;Trans. Am. Math. Soc.,1968

4. On the hamiltonian index of a graph;Chartrand;Stud. Sci. Math Hung.,1973

5. A result on hamiltonian line graphs involving restrictions on induced subgraphs;Veldman;J. Graph Theory,1988

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