Product Graphs: Structure and Recognition
- W. Imrich, S. Klavžar
- Computer Science
- 14 April 2000
Basic Concepts. Hypercubes. Hamming Graphs. Cartesian Products. Strong and Direct Products. Lexicographic Products. Fast Recognition Algorithms. Invariants. Appendices. Bibliography. Indexes.
Handbook of Product Graphs, Second Edition
- R. Hammack, W. Imrich, S. Klavžar
- Mathematics
- 3 June 2011
Handbook of Product Graphs, Second Edition examines the dichotomy between the structure of products and their subgraphs. It also features the design of efficient algorithms that recognize products…
Graphs S(n, k) and a Variant of the Tower of Hanoi Problem
- S. Klavžar, Uroš Milutinović
- Mathematics
- 1 March 1997
For any n ≥ 1 and any k ≥ 1, a graph S(n, k) is introduced. Vertices of S(n, k) are n-tuples over {1, 2,. . . k} and two n-tuples are adjacent if they are in a certain relation. These graphs are…
Domination Game and an Imagination Strategy
- B. Brešar, S. Klavžar, D. Rall
- MathematicsSIAM Journal on Discrete Mathematics
- 1 August 2010
It is proved that for any graph $G, $\gamma_g(G)-1\leq\gamma'_g (G), and that most of the possibilities for mutual values of $G and $G$ can be realized, and a lower bound on the game domination number of an arbitrary Cartesian product is proved.
The Tower of Hanoi - Myths and Maths
- A. M. Hinz, S. Klavžar, Uroš Milutinović, C. Petr
- Computer Science
- 31 January 2013
This is the first comprehensive monograph on the mathematical theory of the solitaire game The Tower of Hanoi which was invented in the 19th century by the French number theorist douard Lucas and contains a thorough, largely self-contained presentation of the essential mathematical facts with complete proofs.
The distinguishing number of Cartesian products of complete graphs
- W. Imrich, J. Jerebic, S. Klavžar
- MathematicsEuropean journal of combinatorics (Print)
- 1 May 2008
1-perfect codes in Sierpiński graphs
- S. Klavžar, Uroš Milutinović, C. Petr
- Mathematics, Computer ScienceBulletin of the Australian Mathematical Society
- 1 December 2002
It is proved that the graphs S (n, κ) possess unique 1-perfect codes, thus extending a previously known result for Hn, and an efficient decoding algorithm is presented.
Stern polynomials
- S. Klavžar, Uroš Milutinović, C. Petr
- MathematicsAdvances in Applied Mathematics
- 1 July 2007
Structure of Fibonacci cubes: a survey
- S. Klavžar
- MathematicsJournal of combinatorial optimization
- 1 May 2013
A survey on Fibonacci cubes is given with an emphasis on their structure, including representations, recursive construction, hamiltonicity, degree sequence and other enumeration results, and their median nature that leads to a fast recognition algorithm is discussed.
Distinguishing Cartesian powers of graphs
- W. Imrich, S. Klavžar
- MathematicsJournal of Graph Theory
- 1 November 2006
It is shown that the distinguishing number of the square and higher powers of a connected graph G 6= K2,K3 with respect to the Cartesian product is 2 and d(G¤H) = 2 if G and H are relatively prime.
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