The q-rung orthopair fuzzy set is a powerful tool for depicting fuzziness and uncertainty, as compared to the Pythagorean fuzzy model. The aim of this paper is to present q-rung orthopair fuzzy competition graphs (q-ROFCGs) and their generalizations, including q-rung orthopair fuzzy k-competition graphs, p-competition q-rung orthopair fuzzy graphs and m-step q-rung orthopair fuzzy competition graphs with several important properties. The study proposes the novel concepts of q-rung orthopair fuzzy cliques and triangulated q-rung orthopair fuzzy graphs with real-life characterizations. In particular, the present work evolves the notion of competition number and m-step competition number of q-rung picture fuzzy graphs with algorithms and explores their bounds in connection with the size of the smallest q-rung orthopair fuzzy edge clique cover. In addition, an application is illustrated in the soil ecosystem with an algorithm to highlight the contributions of this research article in practical applications.