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- Boris Horvat
- 2009

The terminal matrix is the distance matrix between all pairs of valence one vertices of a given graph and the terminal polynomial is the characteristic polynomial of the terminal matrix. Star-like graphs are connected graphs with at most one vertex of degree 3 d . The recursive formula that calculates the terminal polynomial of a star-like graph is given.… (More)

The dilation coefficient of a graph representation is defined as the quotient of the longest and the shortest edge representation. The minimum of the dilation coefficients over all planar representations of a graph G is called the dilation coefficient of the graph G. The dilation coefficient of different planar representations of complete graphs is… (More)

- Boris Horvat, Tomaz Pisanski
- Discrete Mathematics
- 2010

- Boris Horvat, Jan Kratochvíl, Tomaz Pisanski
- IWOCA
- 2010

Some graphs admit drawings in the Euclidean k-space in such a (natural) way, that edges are represented as line segments of unit length. Such drawings will be called k dimensional unit distance representations. When two non-adjacent vertices are drawn in the same point, we say that the representation is degenerate. The dimension (the Euclidean dimension) of… (More)

- Boris Horvat, Tomaz Pisanski, Arjana Zitnik
- Graphs and Combinatorics
- 2012

- Boris Horvat, Tomaz Pisanski
- Ars Comb.
- 2012

- Bojan Tomic, Boris Horvat, Nemanja Jovanovic
- International Journal on Artificial Intelligence…
- 2012

1250013-1 Rule engines, business rule management systems and other rule-based systems used today widely utilize methods, techniques and technologies from the era of expert systems. Unfortunately, this doesn't seem to be the case when it comes to explanation facilities. Nowadays, the use of explanation facilities seems more important than ever. Business rule… (More)

We have constructed graphical (qualitative and visual) representations of DNA sequences as 2D maps and their numerical (quantitative and computational) analysis. The maps are obtained by transforming the four-letter sequences (where letters represent the four nucleic bases) via a spiral representation over triangular and square cells grids into a four-color… (More)

In 1950 a class of generalized Petersen graphs was introduced by Coxeter and around 1970 popularized by Frucht, Graver and Watkins. The family of I-graphs mentioned in 1988 by Bouwer et al. represents a slight further albeit important generalization of the renowned Petersen graph. We show that each I-graph I(n, j, k) admits a unit-distance representation in… (More)

s of the 6th Slovenian International Conference on Graph Theory Bled’07∗ Bled, Slovenia: 24–30 June 2007 * Includes abstracts from the PASCAL Workshop on Graph Theory and Machine Learning Bled’07 c © 2007, DMFA – založništvo – 1677 Abstracts of the 6th Slovenian International Conference on Graph Theory Bled’07 Bled, Slovenia: 24–30 June 2007 Editors: Tomaž… (More)