The spectrum of the hyper-star graphs and their line graphs

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KARIMI F.; Mirafzali S.M.

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ISSN: 2588-4824

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Paper Information

Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2020 | Volume:5 | Issue:21 Page(s): 125-132

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Title

The spectrum of the hyper-star graphs and their line graphs

Author(s)

KARIMI F. | Mirafzali S.M. | Issue Writer Certificate

Keywords

HypercubeQ1

Hyper-star graphQ1

SpectrumQ1

Line graphQ1

Integral graphQ1

Abstract

Let n 1 be an integer. The Hypercube Qn is the graph whose vertex set is f0; 1gn, where two n-tuples are adjacent if they differ in precisely one coordinate. This graph has many applications in Computer sciences and other area of sciences. In the graph Qn, the layer Lk is the set of vertices with exactly k 1’ s, namely, vertices of weight k, 1 k n. The Hyper-star graph B(n; k) is the subgraph of Qn induced by layers Lk and Lk+1; 0 < k < n. In this paper, we determine the Spectrum of the hyperstar graph B(n; k) and L(B(n; k)), where L(B(n; k)) is the Line graph of the graph B(n; k). In particular, we show that the graph L(B(n; k)) is an Integral graph, that is, all of its eigenvalues are integers. In this paper, we investigate some of the algebraic properties of the graph B(n; k) and its Line graph L(B(n; k)). In particular, we determine the Spectrum of these graphs.

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APA: Copy

KARIMI, F., & Mirafzali, S.M.. (2020). The spectrum of the hyper-star graphs and their line graphs. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 5(21 ), 125-132. SID. https://sid.ir/paper/257241/en

Vancouver: Copy

KARIMI F., Mirafzali S.M.. The spectrum of the hyper-star graphs and their line graphs. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2020;5(21 ):125-132. Available from: https://sid.ir/paper/257241/en

IEEE: Copy

F. KARIMI, and S.M. Mirafzali, “The spectrum of the hyper-star graphs and their line graphs,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 5, no. 21 , pp. 125–132, 2020, [Online]. Available: https://sid.ir/paper/257241/en

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