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TCS-604 : Graph Theory Books & references

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Unit- I 
 Graphs, Sub  graphs,  some  basic  properties,  various example  of graphs  & their  sub  graphs,  walks, path  &  circuits,  connected  graphs,  disconnected graphs  and  component,  euler  graphs,  various  operation  on  graphs, Hamiltonian paths and circuits, the traveling sales man problem.

Unit- II 
Trees  and  fundamental  circuits,  distance  diameters, radius  and pendent vertices,  rooted  and binary  trees,  on  counting  trees,  spanning  trees, fundamental circuits, finding  all spanning  trees  of  a graph and a weighted graph, algorithms of primes, Kruskal and dijkstra Algorithms.

Unit -III 
Cuts  sets  and  cut  vertices,  some  properties,  all  cut  sets  in  a  graph, fundamental  circuits  and  cut sets  ,  connectivity  and  separability,  network flows,  planer   graphs,  combinatorial  and  geometric dual,    Kuratowski    to  graphs  detection  of  planarity,  geometric  dual  ,  some  more  criterion  of
planarity, thickness and crossings.
Unit -IV 
Vector  space  of  a  graph  and  vectors,  basis  vector,  cut set  vector,  circuit vector,  circuit  and  cut  set  verses  subspaces,  orthogonal  vectors  and subspaces, incidence matrix  of graph, sub matrices of A(G),  circuit  matrix,  cut  set  matrix,  path  matrix  and  relationships among  A,  B ,  and  C , fundamental circuit  matrix and rank of  B, adjacency matrices, rank- nullity theorem .

Unit -V 
Coloring  and  covering  and  partitioning   of  a  graph,  chromatic  number, chromatic partitioning, chromatic polynomials,  matching, covering, four color problem,  Directed  graphs, some  type  of directed  graphs,  Directed  paths, and  connectedness, Euler  digraphs,  trees with  directed  edges, fundamental
circuits in digraph, matrices  A, B and C  of digraphs adjacency matrix  of  a digraph,,  enumeration,  types  of  enumeration,  counting  of    labeled  and unlabeled  trees,  polya’s   theorem, graph enumeration with polya’s  theorem. Graph theoretic algorithm  must be provided wherever required  to solve  the problems .

1.  Deo, N: Graph theory, PHI
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2.  Harary, F: Graph Theory, Narosa
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3.  Bondy and Murthy: Graph theory and application. Addison Wesley.


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