The Minimum Covering Schultz Energy

In this manuscript, we introduce the concept of minimum covering schultz energy of a graph using adjacency, vertex degree and distance between the vertices. This measure extends the classical schultz energy by incorporating the idea of a minimum vertex covering providing a more informative representation of graph structure. We compute the minimum covering schultz energy for several standard graphs including complete graph, cocktail party graph, star graph and complete bipartite graph. Furthermore, we establish general lower and upper bounds for the minimum covering schultz energy. These results contribute to a better understanding of the relationship between graph coverings, distance-based measures and spectral properties.

Schultz Energy, Schultz Matrix, Schultz Eigenvalues.

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