#### Filter Results:

- Full text PDF available (11)

#### Publication Year

1980

2005

- This year (0)
- Last 5 years (0)
- Last 10 years (0)

#### Publication Type

#### Co-author

#### Journals and Conferences

Learn More

- Siemion Fajtlowicz
- Discrete Mathematics
- 1988

- Paul ErdÃ¶s, Siemion Fajtlowicz, Alan J. Hoffman
- Networks
- 1980

The purpose of this paper is to prove that, with the exception of C 4 , there are no graphs of diameter 2 and maximum degree d with d 2 vertices . On one hand our paper is an extension of [4] where it was proved that there are at most four Moore graphs of diameter 2 (i .e . graphs of diameter 2, maximum degree d, and d2 + 1 vertices) . We also use theâ€¦ (More)

- Siemion Fajtlowicz
- Journal of Graph Theory
- 1988

- Paul ErdÃ¶s, Siemion Fajtlowicz
- Combinatorica
- 1981

Let G=G(n) be a graph of n vertices. Let X=X(G) denote its chromatic number and a=o(G) the largest integer I so that G contains a subdivision of K, i.e . a(G)=1 is the largest integer such that G contains a subgraph homeomorphic with complete graph of l vertices . Let us put H(G)= X(G) and H(n)=max H(G(n)) o (G) G(n) HajÃ³s [10] conjectured that H(n)=1 andâ€¦ (More)

- John Adrian Bondy, Paul ErdÃ¶s, Siemion Fajtlowicz
- Discrete Mathematics
- 1999

The independence number of the graph of a fullerene, the size of the largest set of vertices such that no two are adjacent (corresponding to the largest set of atoms of the molecule, no pair of which are bonded), appears to be a useful selector in identifying stable fullerene isomers. The experimentally characterized isomers with 60, 70 and 76 atomsâ€¦ (More)

We continue the discussion of three topics initiated in the first part of this paper starting with mathematical aspects of the machine intelligence debate initiated in the books of Roger Penrose. Stability Sorting Patterns are by-products of Minuteman, a fullerene version of Graffiti which led to the discovery of a new representation and characterization ofâ€¦ (More)

- Siemion Fajtlowicz
- Combinatorica
- 1984

We shall discuss here some cases in which (1) becomes an equality. 2 Theorem. I f q ~ p then = implies that 3 q 2 p . ~ 5 . For all natural numbers n p + q Pl and ql such that 3 q l 2 p l = 5 there is a unique connected graph G with P = P l , ~t 2 q=q~ a n d = ~ . n p + q 2 1. Since graphs satisfying = must have a large chromatic number n p + q and a highâ€¦ (More)

- Ermelinda DeLaViÃ±a, Siemion Fajtlowicz, William Waller
- Graphs and Discovery
- 2001

We discuss a conjecture of J. R. Griggs relating the maximum number of leaves in a spanning tree of a simple, connected graph to the order and independence number of the graph. We prove a generalization of this conjecture made by the computer program Graffiti, and discuss other similar conjectures, including several generalizations of the theorem that theâ€¦ (More)

- Siemion Fajtlowicz, Peter E. John, Horst Sachsb
- 2005

In August 2003 the computer program GRAFFITI made conjecture 1001 stating that for any benzenoid graph, the size of a maximum matching equals the number of positive eigenvalues. Later, the authors learned that this conjecture was already known in 1982 to I. Gutman (Kragujevac). Here we present a proof of this conjecture and of a related theorem. The resultsâ€¦ (More)