The double-star line graph is a graph built from two complete graphs of order a+1 that share a common vertex, for every positive integer a ≥ 1. In this article, we investigate concepts of energy and energy based on the Mostar index of Dsa and LDsa graphs and provide a low bound for energies. We obtain general formulas for energies of Dsa, LDsa, MoDsa, and MoLDsa. This study obtains general formulas for the Mostar energy and energy of Dsa and LDsa. Using these formulas does not require calculating eigenvalues, and we show that the energy of these graphs only depends on a, the Number of pendeng edges. We compare energies and find relationships between them. Also, we determine the highest and lowest energy. We display the obtained results, numerically and graphically and compare energies graphically.