Tentative Syllabus:
Module-1: Preliminaries & History
Graphs & their representations; Basic concepts: adjacency, incidence, neighbors & degrees; Subgraphs & supergraphs; Isomorphisms & automorphisms; Degree sequences; Special graph families; Walks, trails, paths & cycles; Connected vs disconnected graphs; Eulerian tours (the birth of graph theory) vs Hamiltonian cycles
Module-2: Forests, Trees & Cycles
Module-3: Connectivity
Module-4: Planarity
Module-5: Colorings
Module-6: Matchings
Module-7: Directed graphs (aka Digraphs)