Graph Theory with Applications to Engineering and Computer by Narsingh Deo

By Narsingh Deo

This impressive introductory remedy of graph thought and its purposes has had a longevity within the guide of complex undergraduates and graduate scholars in all components that require wisdom of this topic. the 1st 9 chapters represent an outstanding total advent, requiring just some wisdom of set thought and matrix algebra. themes comprise paths and circuits, timber and primary circuits, planar and twin graphs, vector and matrix illustration of graphs, and comparable subjects.
The final six chapters are extra complex, masking graph conception algorithms and machine courses, graphs in switching and coding idea, electric community research by way of graph idea, graph thought in operations study, and extra. teachers may possibly mix those chapters with the previous fabric for classes in quite a few fields, together with electric engineering, desktop technology, operations study, and utilized arithmetic.

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1-5 Graph of Königsberg bridge problem. The Königsberg bridge problem is the same as the problem of drawing figures without lifting the pen from the paper and without retracing a line (Problems 2-1 and 2-2). We all have been confronted with such problems at one time or another. Utilities Problem: There are three houses (Fig. 1-6) H1, H2, and H3, each to be connected to each of the three utilities—water (W), gas (G), and electricity (E)—by means of conduits. Is it possible to make such connections without any crossovers of the conduits?

R. Hamilton (1805-1865). In the year 1859 he invented a puzzle and sold it for 25 guineas to a game manufacturer in Dublin. The puzzle consisted of a wooden, regular dodecahedron (a polyhedron with 12 faces and 20 corners, each face being a regular pentagon and three edges meeting at each corner; see Fig. 2-21). The corners were marked with the names of 20 important cities: London, NewYork, Delhi, Paris, and so on. The object in the puzzle was to find. a route along the edges of the dodecahedron, passing through each of the 20 cities exactly once [1-12].

The number of edges in a path is called the length of a path. It immediately follows, then, that an edge which is not a self-loop is a path of length one. It should also be noted that a self-loop can be included in a walk but not in a path (Fig. 2-8). The terminal vertices of a path are of degree one, and the rest of the vertices (called intermediate vertices) are of degree two. This degree, of course, is counted only with respect to the edges included in the path and not the entire graph in which the path may be contained.

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