For a positive integer k≥2\documentclass[12pt]{minimal}
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\begin{document}$$k\ge 2$$\end{document}, the radio k-coloring problem is an assignment L of non-negative integers (colors) to the vertices of a finite simple graph G satisfying the condition |L(u)-L(v)|≥k+1-d(u,v)\documentclass[12pt]{minimal}
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\begin{document}$$|L(u)-L(v)| \ge k+1-d(u,v)$$\end{document}, for any two distinct vertices u, v of G and d(u, v) being distance between u, v. The span of L is the largest integer assigned by L, while 0 is taken as the smallest color. An rck\documentclass[12pt]{minimal}
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\begin{document}$$rc_k$$\end{document}-coloring on G is a radio k-coloring on G of minimum span which is referred as the radio k-chromatic number of G and denoted by rck(G)\documentclass[12pt]{minimal}
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\begin{document}$$rc_k(G)$$\end{document}. An integer h, 0<h<rck(G)\documentclass[12pt]{minimal}
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\begin{document}$$0<h<rc_k(G)$$\end{document}, is a hole in a rck\documentclass[12pt]{minimal}
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\begin{document}$$rc_k$$\end{document}-coloring on G if h is not assigned by it. In this paper, we construct a larger graph from a graph of a certain class by using a combinatorial property associated with (k-1)\documentclass[12pt]{minimal}
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\begin{document}$$(k-1)$$\end{document} consecutive holes in any rck\documentclass[12pt]{minimal}
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\begin{document}$$rc_k$$\end{document}-coloring of a graph. Exploiting the same property, we introduce a new graph parameter, referred as (k-1)\documentclass[12pt]{minimal}
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\begin{document}$$(k-1)$$\end{document}-hole index of G and denoted by ρk(G)\documentclass[12pt]{minimal}
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\begin{document}$$\rho _k(G)$$\end{document}. We also explore several properties of ρk(G)\documentclass[12pt]{minimal}
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\begin{document}$$\rho _k(G)$$\end{document} including its upper bound and relation with the path covering number of the complement Gc\documentclass[12pt]{minimal}
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\begin{document}$$G^c$$\end{document}.
