Sourav Mondal (University of Sharjah & SRM Institute of Science and Technology)「Extremal graphs for graph invariants with given parameters」
Graph invariants are properties of a graph that remain unchanged under graph isomorphism, meaning they do not depend on how the graph is labeled or represented. Numerical graph invariants (also known as topological indices) play a crucial role in quantitative structure-activity relationship (QSAR) studies and drug design. Since their inception, numerous invariants based on parameters such as degree, distance, and eigenvalues have been introduced in the literature. A contemporary research trend in this area focuses on characterizing extremal structures within various families of graphs. We explore extremal graphs for degree-based and graph-spectrum-based invariants across different graph families, including chemical trees, unicyclic and bicyclic graphs, chain graphs, and bipartite graphs. We characterize extremal graphs for given graph parameters, such as order, size, number of leaves, chromatic number, clique number, matching number, domination number, and the number of cut vertices. As topological indices can model the physicochemical properties of molecules, understanding these extremal graphs provides valuable insights into structures with optimal properties.