Modern Applied Algebra

Introduction Definition of a Graph, Simple Graph, Konigsberg bridge problem, Utilities problem, Finite and Infinite graphs, Regular graph, Matrix representation of graphs Adjacency matrix, Incidence matrix and examples; Paths and Circuits Isomorphism, Sub graphs, Walk, Path, Circuit, Connected graph, Euler line and Euler graph; Operations on graphs Union of two graphs, Intersecton of two graphs and ring sum of two graphs; Hamiltonian circuit, Hamiltonian path, Complete graph, Traveling salesmen problem. Trees and fundamental circuits, cutsets.