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Wilfried Imrich (born 25 May 1941) is an Austrian mathematician working mainly in graph theory.He is known for his work on graph products, and authored the books Product Graphs: Structure and Recognition (Wiley, 2000, with Sandi Klavžar), [1] Topics in graph theory: Graphs and their Cartesian Products (AK Peters, 2008, with Klavžar and Douglas F. Rall), [2] and Handbook of Product Graphs ...
Klavžar's research concerns graph products, metric graph theory, chemical graph theory, graph domination, and the Tower of Hanoi. Together with Wilfried Imrich and Richard Hammack, he is the author of the book Handbook of Product Graphs (CRC Press, 2011).
In graph theory, a graph product is a binary operation on graphs. Specifically, it is an operation that takes two graphs G 1 and G 2 and produces a graph H with the following properties: The vertex set of H is the Cartesian product V ( G 1 ) × V ( G 2 ) , where V ( G 1 ) and V ( G 2 ) are the vertex sets of G 1 and G 2 , respectively.
If a connected graph is a Cartesian product, it can be factorized uniquely as a product of prime factors, graphs that cannot themselves be decomposed as products of graphs. [2] However, Imrich & Klavžar (2000) describe a disconnected graph that can be expressed in two different ways as a Cartesian product of prime graphs:
The strong product is one of several different graph product operations that have been studied in graph theory. The strong product of any two graphs can be constructed as the union of two other products of the same two graphs, the Cartesian product of graphs and the tensor product of graphs. An example of a strong product is the king's graph ...
Pages in category "Graph products" The following 12 pages are in this category, out of 12 total. This list may not reflect recent changes. ...
The tensor product of graphs. In graph theory, the tensor product G × H of graphs G and H is a graph such that the vertex set of G × H is the Cartesian product V(G) × V(H); and; vertices (g,h) and (g',h' ) are adjacent in G × H if and only if. g is adjacent to g' in G, and; h is adjacent to h' in H.
The lexicographic product of graphs. In graph theory, the lexicographic product or (graph) composition G ∙ H of graphs G and H is a graph such that the vertex set of G ∙ H is the cartesian product V(G) × V(H); and; any two vertices (u,v) and (x,y) are adjacent in G ∙ H if and only if either u is adjacent to x in G or u = x and v is ...