Titlebook: Line Graphs and Line Digraphs; Lowell W. Beineke,Jay S. Bagga Book 2021 Springer Nature Switzerland AG 2021 Line graphs.Line digraphs.Alge

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Iterated Line Digraphsne step, more interesting things can happen, one being that connectedness is not necessarily preserved. Another instance is that a digraph can be isomorphic to its second iterated line digraph but not to its first. In more general terms, there are digraphs for which, after a while, the sequence of i

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Total Graphs and Total Digraphsrch into variations and generalizations of the subject. In this, the first of several chapters on such topics, instead of just the edges of a given graph becoming the vertices of a new graph, both the vertices and the edges of the original become vertices. The new graph is called the total graph of

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Path Graphs and Path Digraphsthese vertices being given by their having a path of length 1 in common and their union being either a path or cycle of length 3. After proving some basic results, we turn to the characterization of path graphs, the main theorem being an analogue of Krausz’s partition characterization for line graph

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Super Line Graphs and Super Line Digraphsf these vertices be adjacent if at least one of the edges in one set is adjacent in . to at least one of those in the other set. This new graph is called a line graph of index 2. Naturally, line graphs of index . are defined analogously, and they constitute the subject of this chapter and have the n

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Lowell W. Beineke,Jay S. BaggaThe first monograph devoted exclusively to Line Graphs and Line Digraphs.Provides a comprehensive, historical and up-to-date reference on the subject.Covers line graphs and line digraphs from their or

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Spectral Properties of Line Graphshs’s theorem which states that eigenvalues of the adjacency matrix of a line graph are never less than −2. This feature pervades this chapter, culminating in a powerful theorem of Cameron, Goethals, Seidel, and Shult on root systems.