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

Hiatal-Hernia

换话题

Line Graph Isomorphisms the edges of a graph with three edges with a common vertex and a graph with three edges forming a cycle. As shown by Hassler Whitney, this mapping not only preserves adjacency of edges, but these two are the only connected non-isomorphic graphs with this property. Whitney also proved that there are

GORGE

prostate-gland

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.

专横

不合

Connectivity of Line Graphs graph. Most of the results provide equalities or inequalities involving some of the three classical parameters of the connectivity, the edge-connectivity, and the minimum degree of both graphs and line graphs. The last section applies some of these concepts to iterated line graphs.

alcohol-abuse

Traversability in Line Graphscterizations. We then turn to the subject of Hamiltonian graphs. It is not hard to show that the line graph of a Hamiltonian graph is Hamiltonian, but as one would expect, determining which line graphs are Hamiltonian is a difficult problem. The fourth section is devoted to aspects of an outstanding

耐寒

Colorability in Line Graphsns. A basic relationship is the fact that coloring the edges of a graph is equivalent to coloring the vertices of its line graph. In fact, this fact provides us with a line graph version of the four color theorem. The line graphs of cubic graphs constitute an interesting family on their own: it is k

GROWL

Distance and Transitivity in Line Graphsric concepts of diameter, radius, and center. Some of the results involve connections for these quantities between graphs and their line graphs, and what happens to their values in iterated line graphs. The center of a graph is also defined in a natural way, and some intriguing results on the center

Sleep-Paralysis

Fundamentals of Line Digraphs by Harary and Norman and didn’t appear until 1960. In this chapter, line digraphs are defined, after which some of their elementary directed properties are established, including some involving connectedness, degrees, paths and cycles, and distance. This is followed by some of the nicest results on