Can some people suggest some good syllabus for graph theory, advanced graph theory and discrete mathematics for Computer science Engineering students
Basic Concepts: Graphs and digraphs, incidence and adjacency matrices, isomorphism, the automorphism group; Trees: Equivalent definitions of trees and forests, Cayley's formula, the Matrix-Tree theorem, minimum spanning trees; Connectivity: Cut vertices, cut edges, bonds, the cycle space and the bond space, blocks, Menger's theorem; Paths and Cycles: Euler tours, Hamilton paths and cycles, theorems of Dirac, Ore, Bondy and Chvatal, girth, circumference, the Chinese Postman Problem, the Traveling Salesman problem, diameter and maximum degree, shortest paths; Matchings: Berge's Theorem, perfect matchings, Hall's theorem, Tutte's theorem, Konig's theorem, Petersen's theorem, algorithms for matching and weighted matching (in both bipartitie and general graphs), factors of graphs (decompositions of the complete graph), Tutte's f-factor theorem; Extremal problems: Independent sets and covering numbers, Turan's theorem, Ramsey theorems; Colorings: Brooks theorem, the greedy algorithm, the Welsh-Powell bound, critical graphs, chromatic polynomials, girth and chromatic number, Vizing's theorem; Graphs on surfaces: Planar graphs, duality, Euler's formula, Kuratowski's theorem, toroidal graphs, 2-cell embeddings, graphs on other surfaces; Directed graphs: Tournaments, directed paths and cycles, connectivity and strongly connected digraphs, branchings; Networks and flows: Flow cuts, max flow min cut theorem, perfect square; Selected topics: Dominating sets, the reconstruction problem, intersection graphs, perfect graphs, random graphs.
Now what would you like, graph theory or advanced graph theory? You used both, pick one. One assumes an understanding of Graph Theory, the other does not. I think if you want àdvanced`graph theory, I`d go with a selection of the topics from Rakesh`s answer (depending on the direction of the material). Also it would depend on what you mean by engineering on how you pick these. If you mean computing science (not engineering) then I would take the more applicable ones relating to matching theory and Hall`s theorem to be fundamental. If you want pure engineering, I`d go with the network flow approach as circuit design can often affiliate to such.
These are some suggested reading for discrete mathematics and graph theory :
1. J.P. Trembley and R.P.Manohar, Discrete Mathematical Structures with Applications to Computer Science, McGraw Hill.
2. Dornhoff and Hohn, Applied Modern Algebra, McMillan.
3. N. Deo, Graph Theory with Applications to Engineering and Computer Science, PHI.
4. R. Johnsonbaugh, Discrete Mathematics, Pearson Education, 2001.
5. R. P. Grimaldi, Discrete and Combinatorial Mathematics, Pearson Education, 1999.
6. C.L. Liu, Elements of Discrete Mathematics, McGraw-Hill.
7. Rosen, Discrete Mathematics, Tata McGraw Hill.
Who are Interested in Graph Theory, they compulsory bought some of the following Text Books.
1. F. Harary, Graph Theory
2. Narsing Deo, Introduction to Graph Theory and It's Applications to Engineering
3. John Clerk, Introduction to Graph Theory
I have already completed rosen keneth 60 % as discrete mathematics in syllabus i want syllabus for advanced graph theory Computer science
You can see these links:
Syllabus - Introduction to Graph Theory MTH548 - Spring 20000 ...
http://www.math.uri.edu/~eaton/MTH548F03.htm
Syllabus for MATH 313: Graph Theory - HWS Department of ...
http://math.hws.edu/eking/s13syllabus
Graph Theory with Applications to Engineering and Computer Science by Deo Narsingh. This is the best book I have ever encountered.
Meet experts and other researchers at graph theory events...We are hosting the following one...
http://event.cs.usm.my/IWGA2015/
Here is model syllabus for the computer science students. From the syllabus of University of Calicut, Kerala, India.
Introduction to graphs, definitions, sub graphs, paths and cycles, matrix representation of graphs, Euler tours, Chinese Postman problem, Planar graphs, Euler's formula, platonic bodies, applications of Kuratowski's theorem, Hamiltonian graphs, graph coloring and chromatic polynomials, map coloring.
Trees, definitions and properties, rooted trees, trees and sorting, weighted trees and prefix codes, bi connected components and articulation points, Kruskal's and Prim's algorithms for minimal spanning trees.
Dijkstra’s shortest path algorithm - bellman ford algorithm, all pair shortest path,Floyed Warshall algorithm, the max flow min cut theorem - maximum bipartite matching.
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