IJLTEMAS International Journal of Latest Technology in Engineering, Management & Applied Science (IJLTEMAS) IJLTEMAS 2278-2540 IJLTEMAS 382 10.51583/IJLTEMAS.2026.150900031 Mathematics - Graph Theory and Combinotrics The Minimum Covering Schultz Energy R S Indumathi Associate Professor, Department of MathematicsMaharaja Institute of Technology Mysore, Mandya, Karnataka, India – 571477 Affiliated to Visvesvaraya Technological University, Belagavi, Karnataka, India – 590018 India Kanna M R Rajesh Associate Professor, Department of Mathematics Maharani’s Science College for Wome (Autonomous), J.L.B. Road, Mysuru, Karnataka, India – 570005 India K Nataraj Assistant Professor, Department of Mathematics Maharaja Institute of Technology Mysore, Mandya, Karnataka, India – 571477 Affiliated to Visvesvaraya Technological University, Belagavi, Karnataka, India – 590018 India S Purushothama Associate Professor, Department of Mathematics Maharaja Institute of Technology Mysore, Mandya, Karnataka, India – 571477 Affiliated to Visvesvaraya Technological University, Belagavi, Karnataka, India – 590018 India 15 9 393 409 16 09 2026 21 09 2026 03 10 2026 Schultz Energy Schultz Matrix Schultz Eigenvalues. Abstract

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.

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