Graph Theory Book By Harary Pdf Download
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How to Download Graph Theory by Frank Harary PDF for Free
Graph theory is a branch of mathematics that studies the properties and applications of graphs, which are structures consisting of nodes and edges. Graph theory has many applications in various fields, such as computer science, physics, chemistry, biology, social sciences, and more.
One of the classic books on graph theory is Graph Theory by Frank Harary, which was first published in 1969. This book covers the basic concepts and results of graph theory, such as connectivity, partitions, traversability, line graphs, factorization, coverings, planarity, colorability, matrices, groups, enumeration, and digraphs. The book also includes many examples and exercises to illustrate the theory and practice of graph theory.
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What is Graph Theory
Graph theory is a branch of mathematics that studies the properties and applications of graphs. A graph is a structure that consists of a set of nodes (also called vertices or points) and a set of edges (also called links or lines) that connect some pairs of nodes. Graphs can be used to model many phenomena in the real world, such as networks, maps, circuits, games, puzzles, and more.
Graph theory has a long history, dating back to the 18th century, when the Swiss mathematician Leonhard Euler solved the famous Seven Bridges of KÃnigsberg problem. The problem asked whether it was possible to walk through the city of KÃnigsberg (now Kaliningrad) and cross each of its seven bridges exactly once. Euler showed that this was impossible by representing the city as a graph and proving that such a walk (called an Eulerian path) exists only if the graph has no nodes with an odd number of edges (called odd-degree nodes).
Since then, graph theory has developed into a rich and diverse field of mathematics, with many branches and subfields. Some of the main topics in graph theory are:
Connectivity: This refers to how well a graph is connected, or how easy it is to move from one node to another in the graph. For example, a connected graph is one where there is a path between any two nodes, while a disconnected graph has at least two components that are not connected by any edge. There are also other measures of connectivity, such as cut-vertices, bridges, blocks, and k-connectivity.
Partitions: This refers to how a graph can be divided into smaller parts or subsets of nodes and edges. For example, a bipartite graph is one where the nodes can be partitioned into two sets such that no edge connects two nodes from the same set. There are also other types of partitions, such as cliques, independent sets, dominating sets, and vertex covers.
Traversability: This refers to how a graph can be traversed or visited by following its edges. For example, an Eulerian path is a path that visits every edge exactly once, while a Hamiltonian path is a path that visits every node exactly once. There are also other types of traversals, such as cycles, tours, walks, trails, and circuits.
Line graphs: This refers to graphs that are derived from other graphs by replacing each edge with a node and connecting two nodes if they correspond to adjacent edges in the original graph. For example, the line graph of a cycle is another cycle with the same number of nodes. Line graphs have many applications in chemistry, coding theory, and network analysis.
Factorization: This refers to how a graph can be decomposed into smaller graphs that have some property or structure. For example, a 1-factor of a graph is a subgraph that is a perfect matching (a set of edges that covers every node exactly once). There are also other types of factors, such as k-factors, regular factors, spanning subgraphs, and decompositions.
Coverings: This refers to how a graph can be covered by smaller graphs that have some property or structure. For example, an edge-covering of a graph is a set of edges that covers every node at least once. There are also other types of coverings, such as vertex-coverings, dominating sets, packing problems, and domination problems.
Planarity: This refers to whether a graph can be drawn on a plane without any crossing edges. For example, a tree (a connected graph without cycles) is always planar, while K5 (the complete graph on five nodes) is not planar. Planarity has many applications in map coloring 061ffe29dd