Cm,sk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {C}}^k_{m,s}$$\end{document} as a k-uniform hypergraph and some its properties

Hypergraphs are important data structures that are used abundantly in modern science for analyzing complex and big data. One of the most interesting and highly application in hypergraph theory is the spectral theory that is taken into consideration in recent years. In this paper we introduce Cm,sk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {C}^k_{m,s}$$\end{document} as an extension of the cycle in graph theory which is not a power hypergraph and nor a cored hypergraph. We show that it is regular and odd-bipartite if m is even. Also a necessary and sufficient condition for odd-bipartition whenever m is odd is presented. Finally we give some spectral properties of it.