Book Name : Schaum’s Outline Of Theory and Problems of Graph Theory
Author Name : V. K. RAMAKRISHNAN. Ph. D
Book Format : PDF
Size : 30 MB +
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| Graph theory by schaum series pdf download |
Description : Embark on a captivating exploration of Graph Theory with "Schaum's Outline of Graph Theory" by Shaun Series. This comprehensive guide takes readers on a journey through the intricate world of graphs and digraphs, unraveling the fundamental concepts and applications that underpin this fascinating field of study. The book commences with a solid foundation, introducing the basics of graph theory, including graph isomorphism, subgraphs, degrees, adjacency matrices, and incidence matrices. Moving beyond the basics, readers delve into the realm of connectivity, where they encounter paths, circuits, cycles, connected graphs, and trees, along with the intriguing concept of strong orientations of graphs. The exploration continues with a focus on Eulerian and Hamiltonian graphs, shedding light on their unique properties and applications. Optimization involving trees is thoroughly examined, covering minimum weight spanning trees, maximum weight branchings, minimum weight arborescences, and the application of matroids through the greedy algorithm. Shortest path problems, a vital aspect of graph theory, are explored in depth, addressing two shortest path algorithms, the Steiner network problem, and facility location problems. The book further navigates through the realm of flows, connectivity, and combinatorics, offering insights into flows in networks, Menger's theorem, and applications to combinatorics. Matching problems and factors are then unveiled, including discussions on the optimal assignment problem, the traveling salesperson problem (TSP), factors, factorizations, and the intriguing Petersen graph. Graph embeddings take center stage in the eighth chapter, with discussions on planar graphs, duality, Hamiltonian plane graphs, maximum flow in planar networks, and an informal treatment of graphs on surfaces. The exploration concludes with a thorough examination of colorings of graphs, covering vertex coloring, edge coloring, and the coloring of planar graphs. With clear explanations, illustrative examples, and a wealth of applications, "Schaum's Outline of Graph Theory" equips readers with a comprehensive understanding of graph theory concepts and their diverse applications, making it an invaluable resource for both students and enthusiasts of this captivating mathematical discipline.