For a positive integer 𝑘≥2, 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), 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-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). An integer h, 0<ℎ<𝑟𝑐𝑘(𝐺), is a hole in a 𝑟𝑐𝑘-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) consecutive holes in any 𝑟𝑐𝑘-coloring of a graph. Exploiting the same property, we introduce a new graph parameter, referred as (𝑘−1)-hole index of G and denoted by 𝜌𝑘(𝐺). We also explore several properties of 𝜌𝑘(𝐺) including its upper bound and relation with the path covering number of the complement 𝐺𝑐.