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Category: Mathematics Assignment Help

Published on Friday, 08 March 2013 08:34

Written by Super User

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The exhaustive list of topics in Graph Theory in which we provide Help with Homework Assignment and Help with Project is as follows:

• Graphs: Definition of a graph and directed graph, simple graph. Degree of a vertex, regular graph, bipartite graphs, subgraphs, complete graph, complement of a graph, operations of graphs, isomorphism and homomorphism between two graphs, directed graphs and relations.
• Paths and Circuits: Walks, paths and circuits, connectedness of a graph, Disconnected graphs and their components, Konigsberg 7-bridge problem, Around the world problem, Euler graphs, Hamiltonian paths and circuits, Existence theorem for Eulerian and Hamiltonian graphs.
• Trees and Fundamental circuits: Trees and their properties, distance and centre in a tree and in a graph, rooted and binary trees, spanning trees and forest, fundamental circuits, cut sets,  connectivity and separability,1-isomorphism, 2-isomorphism, breadth first and depth first search.
• Matrix representation of graphs:  Incidence matrix and its sub matrices, Reduced incidence matrix, circuit matrix, fundamental circuit  matrix, cut set matrix, fundamental cut set  matrix, path matrix, adjacency matrix of a graph and of digraph.
• Planar and Dual graph: Planar graphs, Euler’s formula, Kuratowski’s graphs, detections of planarity, geometric dual, combinatorial dual.
• Coloring of planar graphs: Chromatic number, independent set of vertices, maximal independent set, chromatic partitioning, dominating set, minimal dominating set, chromatic polynomial, coloring and four colour problem, coverings, machings in a graph.
• Graph Algorithms: Network flows, Ford-Fulkerson algorithm for maximum flow, Dijkstra algorithm for shortest path between two vertices, Kruskal and Prim’s  algorithms for minimum spanning tree.