Applied graph theory
Basic concepts. Basic definitions of linear graphs. Edge sequenses and conectedness. Matrix representation of graphs. special graphs and subgraphs. Connectivity and independence in graphs. Planar graphs. Definitions and concepts of planar graphs. Straight line representation of planar graphs. Criteria for planar graphs. Determination of planarity. Hamilton graphs. Definitions and basic concepts. Cubical graphs. Additional results on Hamilton graphs. Graph coloring. Combinatorial theory. Radom graphs. Application in operations research. Applications in social science and psychology. Applications in physics.
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Connectivity and Independence in Graphs
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adjacency matrix algorithm applications assigned automorphism group basic called Chapter chromatic number colors column combinatorial complete complete graph components concept connected graph consider contains corresponding cubical graph cyclic euler path defined denote the number digraph directed discussed distinct edge sequence edges of G elements enumeration euler path euler's formula example finite formulation function given graph G graph theory hamilton circuit hamilton graph hence homomorphism illustrated incidence matrix integer knight's tour labels length linear graph linear programming method multiple edges n-graph number of edges number of vertices obtained optimal pair of vertices partition permutation planar graph points problem Proof Ramsey's theorem random graphs reader represent representation result section graph set of vertices shown in Figure simple cycle solution specified square structure subgraph subset terminal vertices theorem tree undirected graphs utilized values variables vector vertex set yields zero