Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://project.dml.cz Časopis pro pěstování matematiky, roč. 110 (1985), Praha EDGE ROTATIONS AND DISTANCE BETWEEN GRAPHS

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Abstract. The edge-clique graph K(G) of a graph G is that graph whose vertices correspond to the edges of G and where two vertices of K(G) are adjacent whenever the corresponding edges of G belong to a common clique. It is shown that every edge-clique graph is a clique graph, and that if G is either an interval graph or a line graph, then so too is K(G). An algorithm is provided for determining whether a graph is an edge-clique graph. A new graph called the STP graph is introduced and a relationship involving this graph, the edge-clique graph, and the line graph is presented. The STP graphs are also characterized.

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Abstract.A graph G without isolated vertices is a greatest common subgraph of a set c~ of graphs, all having the same size, ifG is a graph of maximum size that is isomorphic to a subgraph of every graph in ft. A number of results concerning greatest common subgraphs are presented. For several graphical properties ~@, we discuss the problem of determining, for a given graph G with property ~, the existence of two non-isomorphic graphs G 1 and G2 of equal size, also with property ~', such that G is the unique greatest common subgraph of G1 and G 2. In particular, this problem is solved when N is the property of being 2-connected and when N is the property of having chromatic number n.