Chunling Tong1, Senyuan Su1, Yuansheng Yang2
1College of Information Science and Electricity Engineering, Shandong Jiaotong University, Jinan 250357, China
2College of Computer Science, Dalian University of Technology, Dalian 116024, China
Abstract:

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

Marta Na Chen1, Wenchang Chu2
1School of Mathematics and Statistics, Zhoukou Normal University Zhoukou (Henan), China
2Via Dalmazio Birago 9E, Lecce 73100, Italy
Abstract:

By employing Kummer and Thomae transformations, we examine four classes of nonterminating \(_3F_2\)(1)-series with five integer parameters. Several new summation formulae are established in closed form.

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