\((d,1)\)-Total Labelling of Generalized Petersen Graphs \(P(n,k)\)

Chunling Tong,College Of Information Science And Electricity Engineering, Shandong Jiaotong University, Jinan 250357, China ,Senyuan Su,Yuansheng Yang,College Of Computer Science, Dalian University Of Technology, Dalian 116024, China ,College Of Computer Science, Dalian University Of Technology, Dalian 116024, China

doi:10.61091/ars158-02

\((d,1)\)-Total Labelling of Generalized Petersen Graphs \(P(n,k)\)

Chunling Tong, College Of Information Science And Electricity Engineering, Shandong Jiaotong University, Jinan 250357, China + Show 4 more

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https://doi.org/10.61091/ars158-02

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Journal: Ars Combinatoria	Publication Date: Jan 1, 2024
License type: cc-by

#Generalized Petersen Graphs #Petersen Graphs + Show 1 more

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Abstract

In this paper, we investigate the ( d , 1 ) -total labelling of generalized Petersen graphs P ( n , k ) for d ≥ 3 . We find that the ( d , 1 ) -total number of P ( n , k ) with d ≥ 3 is d + 3 for even n and odd k or even n and k = n 2 , and d + 4 for all other cases.

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