Unit 1:
Introduction: Definition of graph-degree of vertex- Regular graphs – Connected graph, complete graphs – Bipartite graph – Euler graph necessary and sufficient conditions for Euler graph-Hamiltonian graph and its properties – Connectivity, vertex connectivity, edge connectivity.Trees – properties of Trees-spanning tree
Unit 2:
Domination theory – Definition of dominating sets in graphs- Domination number- bounds in terms of degree, diameter and girth- product graphs and Vizing’sconjecture
Unit 3:
Changing and unchanging domination – changing vertex removal – changing edge removal – bondage number – unchanging vertex removal – unchanging edge removal
Unit 4:
Four Standard Graph Products – Cartesian Product – Strong Product – Direct Product – Lexicographic Product – distance formula
Unit 5:
Three Fundamental Products – Commutativity property, Associativity property -Projections and Layers