@MISC{Tomanova91amalgamationsand, author = {J. Tomanova}, title = {Amalgamations And Link Graphs Of Cayley Graphs}, year = {1991} }

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Abstract

. The link of a vertex v in a graph G is the subgraph induced by all vertices adjacent to v. If all the links in G are isomorphic to the same graph L, then L is called the link graph of G. We consider the operation of an amalgamation of graphs. Using the construction of the free product of groups with amalgamated subgroups, we give a sufficient condition for a class of link graphs of Cayley graphs to be closed under amalgamations. 1. Introduction The link of a vertex v of a graph G is the subgraph induced by all vertices adjacent to v; we denote it by link (v; G). If all the links in G are isomorphic to the same graph L, then we say that G has a constant link L and L is called the link graph of G. In 1963 Zykov [6] posed the problem of characterizing link graphs. It turned out that the problem is algorithmically unsolvable in the class of all (possibly infinite) graphs, see Bulitko [2]. However, the solution of Zykov's problem is known for certain classes of graphs (for survey see Hel...