Misra A. Graph Theory and Probability. Graph Theory 2011

Textbook in PDF format

Graph Theory Graph and sub graphs, Isomorphic, homomorphism graphs, Paths, Hamiltonian Circuits, Eulerian Graph, Connectivity.
The Bridges of Konigsberg,Transversal, Multi graphs, Labelled graph, Complete, regular and bipartite graphs, planar graphs.
Graph colourings, Chromatic number, Connectivity, Directed graphs, basic definitions, Tree graphs,Binary trees, rooted trees.
Minimal spanning tree, Prim’s algorithm, shortest path.
Propositions and compound propositions, Basic logical operations, Truth tables, Tautologies and Contradictions, Logical equivalence.
Logic gates, Logic circuits, and switching function, Partially ordered set.
Lattice, Boolean algebra, Lattice as Boolean algebra, Application of Boolean algebra to on–off switching theory.
Sample space, events, and probability functions, Examples using counting methods, sampling with or without replacement, Algebra of events.
Conditional probability, partitions of sample space. Theorem of total probability, Baye’s theorem, independence, Random variables.
Probability mass functions, Discrete distributions Binomial, Poisson, geometric. Expectation - mean and variance