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Path graph

The path graph is a tree with two nodes of vertex degree 1, and the other nodes of vertex degree 2. A path graph is therefore a graph that can be drawn so that all of its vertices and edges lie on a single straight line (Gross and Yellen 2006, p. 18).The path graph of length is implemented in the Wolfram Language as PathGraph[Range[n]], and precomputed properties of path graphs are available as GraphData["Path", n]. (Note that the Wolfram Language believes cycle graphs to be path graph, a convention that seems neither standard nor useful.)The path graph is known as the singleton graph and is equivalent to the complete graph and the star graph . is isomorphic to the complete bipartite graph and to .Path graphs are graceful.The path graph has chromatic polynomial, independence polynomial, matching polynomial, and reliability polynomial given by(1)(2)(3)(4)where . These have recurrence equations(5)(6)(7)(8)The line graph of..

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