# Italo José Dejter
**Italo José Dejter** (born 1939 in [Bahía Blanca](https://www.edgepedia.org/bahia-blanca), Argentina) is an Argentine-born mathematician, retired professor at the University of Puerto Rico, Río Piedras, whose work spans algebraic and differential topology, graph theory, coding theory, and design theory[1](https://www.deutsche-biographie.de/1071243624.html?language=en) • [2](https://scholar.google.com/citations?user=sfL2pxgAAAAJ&hl=en). Combinatorial structures are named after him, the Dejter graphs, and he carried out a long research program on perfect and efficient dominating codes in Cayley graphs and integer lattices[3](https://mathworld.wolfram.com/DejterGraph.html) • [2](https://scholar.google.com/citations?user=sfL2pxgAAAAJ&hl=en).
| Key fact | Detail |
|---|---|
| Born | 1939, Bahía Blanca, Argentina (GND authority record 1071243624)[1](https://www.deutsche-biographie.de/1071243624.html?language=en) |
| Doctorate | Ph.D., Rutgers University, New Brunswick, 1975; advisor Ted Edgar Petrie; dissertation on smooth G manifolds and G transversality to CPⁿ[4](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=5831) |
| Academic post | Retired Professor of Mathematics, University of Puerto Rico, Río Piedras, 1 August 1984 to 1 March 2018[5](https://orcid.org/0000-0003-0288-1748) |
| Namesake object | Dejter graph: weakly regular, 112 vertices, 336 edges, obtained by deleting a length-7 Hamming code from the binary 7-cube[3](https://mathworld.wolfram.com/DejterGraph.html) |
| Signature result | Uncountably many parallel total perfect codes in the planar integer lattice, against exactly one 1-perfect code and one total perfect code restricting to total perfect codes of rectangular grid graphs there[6](https://ajc.maths.uq.edu.au/v42.p099) |
| Active through | Journal papers in 2024 and 2026[8](https://researchr.org/alias/italo-j.-dejter) • [9](https://pisrt.org/psrpress/j/odam/2026/issue%201/castling-tree-of-tight-dyck-nests-with-applications-to-odd-and-middle-levels-graphs.pdf) |
## Life and education
Dejter was born in Bahía Blanca, Argentina, in 1939[1](https://www.deutsche-biographie.de/1071243624.html?language=en). His doctoral studies are recorded by the Mathematics Genealogy Project at [Rutgers University](https://www.edgepedia.org/rutgers-university), New Brunswick, with the degree awarded in 1975; his advisor was Ted Edgar Petrie, and the dissertation was *Smooth G Manifolds on a Homotopy Type and G Transversality to CP^n*[4](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=5831). ORCID dates the Rutgers enrollment from 15 August 1970 to 30 May 1975[5](https://orcid.org/0000-0003-0288-1748).
His appointment at the University of Puerto Rico system in San Juan is recorded by ORCID as beginning 1 August 1984 and ending 1 March 2018, with the title Retired Professor ([Mathematics](https://www.edgepedia.org/mathematics))[5](https://orcid.org/0000-0003-0288-1748). A University of Puerto Rico, Río Piedras mathematics department seminar document lists him with the departmental address PR 00936-8377, confirming the Río Piedras affiliation[10](https://math.uprrp.edu/seminarios/abstracts/dejter3.pdf).
## Mathematical work
His [Google Scholar](https://www.edgepedia.org/google-scholar) profile lists his areas as algebraic topology, differential topology, graph theory, coding theory, and design theory[2](https://scholar.google.com/citations?user=sfL2pxgAAAAJ&hl=en).
**Perfect codes in lattices.** A 2003 paper with Oriol Serra, *Efficient dominating sets in Cayley graphs* (Discrete Applied Mathematics 129(2-3): 319-328), appears in this area[8](https://researchr.org/alias/italo-j.-dejter) • [2](https://scholar.google.com/citations?user=sfL2pxgAAAAJ&hl=en). In a later paper in the Australasian Journal of Combinatorics, Dejter showed that the planar integer lattice graph Λ of R² carries an uncountable number of parallel total perfect codes, in contrast with exactly one 1-perfect code in Λ and one total perfect code in Λ restricting to total perfect codes of rectangular grid graphs[6](https://ajc.maths.uq.edu.au/v42.p099) • [14](https://ajc.maths.uq.edu.au/pdf/42/ajc_v42_p099.pdf). The unique total perfect code restricts to total perfect codes of rectangular grid graphs and yields an asymmetric, [Penrose tiling](https://www.edgepedia.org/penrose-tiling) of the plane, connecting the coding-theoretic construction to aperiodic tilings[6](https://ajc.maths.uq.edu.au/v42.p099). He also characterized all cycle products C_m × C_n with parallel total perfect codes, showing that the d-perfect code partitions have as quotient graph the undirected Cayley graph of Z_{2d²+2d+1} with generator set {1, 2d²}[6](https://ajc.maths.uq.edu.au/v42.p099).
**Coding theory and design theory.** In a 2005 Discrete Mathematics paper with Abel A. Delgado, *STS-graphs of perfect codes mod kernel* (295(1-3): 31-47), and related work, Dejter introduced an invariant for extended 1-perfect codes C, the SQS-graph HK(C), where K = Ker(C)[8](https://researchr.org/alias/italo-j.-dejter) • [11](https://arxiv.org/pdf/0903.5049).
**Nonexistence results.** Not all of the program is constructive. Dejter proved that X³_n, the [Cayley graph](https://www.edgepedia.org/cayley-graph) generated by transposition trees of diameter 3, has no efficient dominating sets[12](https://www.arxiv.symmetricfunctions.com/author/italo-j-dejter).
**Perfect distance-dominating sets.** Motivated by a computer-architecture problem, Dejter introduced the perfect distance-dominating set (PDDS) in a graph, a generalization of perfect Lee codes and diameter perfect codes, and used it to state an extension of the long-standing Golomb-Welch conjecture[12](https://www.arxiv.symmetricfunctions.com/author/italo-j-dejter). A related generalization replaces the requirement that each vertex outside S have exactly one neighbor in S with the requirement that it have exactly ℓ neighbors in S, giving efficient dominating ℓ-sets[12](https://www.arxiv.symmetricfunctions.com/author/italo-j-dejter).
## Dejter graphs
The object carrying his name is defined by deletion. The Dejter graph is a weakly regular graph on 112 vertices and 336 edges with regular parameters, obtained by deleting a copy of the length-7 [Hamming code](https://www.edgepedia.org/hamming-code) from the [hypercube graph](https://www.edgepedia.org/hypercube-graph) constructed as a binary 7-cube[3](https://mathworld.wolfram.com/DejterGraph.html).
## How it compares with other graph families
The Dejter graph is a subgraph of the 7-cube, so it sits inside the hypercube family rather than beside it: it inherits the cube's binary-coordinate structure and is described as weakly regular[3](https://mathworld.wolfram.com/DejterGraph.html). Dejter's own work supplies a comparison point of a different kind: his quotient-graph characterizations express code partitions through Cayley graphs of cyclic groups, such as the Cayley graph of Z_{2d²+2d+1} with generators {1, 2d²} for cycle-product total perfect codes[6](https://ajc.maths.uq.edu.au/v42.p099).
## By the numbers
ORCID indexes 37 works for Dejter[5](https://orcid.org/0000-0003-0288-1748). A weak metrics-aggregator source lists an h-index of 10 and 396 citations, with Dejter as corresponding author on *Perfect domination in regular grid graphs*[7](https://doi.org/10.48550/arxiv.0711.4343). The documented publication record runs from the 1975 dissertation[4](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=5831) to a journal paper published 10 April 2026[9](https://pisrt.org/psrpress/j/odam/2026/issue%201/castling-tree-of-tight-dyck-nests-with-applications-to-odd-and-middle-levels-graphs.pdf), a span of about five decades. The namesake graph has 112 vertices and 336 edges[3](https://mathworld.wolfram.com/DejterGraph.html).
## Recent developments
Dejter has remained active. In 2024 he published two papers in Ars Combinatoria, one on a Knuth combinatorial generation problem (160(1): 37-57) and one on total coloring and efficient domination applications to non-Cayley, non-Shreier [vertex-transitive graphs](https://www.edgepedia.org/vertex-transitive-graph) (161(1): 75-87)[8](https://researchr.org/alias/italo-j.-dejter). He also posted 2024 arXiv preprints, including work on efficient total colorings of finite connected simple cubic graphs of girth 4, constructed starting at the 3-cube, with the conjecture that all such colorings arise from four basic operations, and noting that the Robertson 19-vertex (4,5)-cage contains nonefficient total colorings[12](https://www.arxiv.symmetricfunctions.com/author/italo-j-dejter). A March 2024 preprint, arXiv 2403.05643, is authored from the University of Puerto Rico, Río Piedras[13](https://arxiv.org/html/2403.05643). A 2026 paper in the Journal of Discrete and Applied Mathematics, received 28 December 2025 and published 10 April 2026, treats a castling tree of tight Dyck nests with applications to odd and middle-levels graphs[9](https://pisrt.org/psrpress/j/odam/2026/issue%201/castling-tree-of-tight-dyck-nests-with-applications-to-odd-and-middle-levels-graphs.pdf).
## References
1. [Dejter, Italo José, Deutsche Biographie](https://www.deutsche-biographie.de/1071243624.html?language=en)
2. [Italo Dejter, Google Scholar profile](https://scholar.google.com/citations?user=sfL2pxgAAAAJ&hl=en)
3. [Dejter Graph, Wolfram MathWorld](https://mathworld.wolfram.com/DejterGraph.html)
4. [Italo J. Dejter, The Mathematics Genealogy Project](https://www.genealogy.math.ndsu.nodak.edu/id.php?id=5831)
5. [Italo Dejter (0000-0003-0288-1748), ORCID](https://orcid.org/0000-0003-0288-1748)
6. [Perfect domination in regular grid graphs, Australasian Journal of Combinatorics](https://ajc.maths.uq.edu.au/v42.p099)
7. [Perfect domination in regular grid graphs, exa.ai library](https://doi.org/10.48550/arxiv.0711.4343)
8. [Italo J. Dejter, researchr alias page](https://researchr.org/alias/italo-j.-dejter)
9. [Castling tree of tight Dyck nests with applications to odd and middle-levels graphs, Journal of Discrete and Applied Mathematics (2026)](https://pisrt.org/psrpress/j/odam/2026/issue%201/castling-tree-of-tight-dyck-nests-with-applications-to-odd-and-middle-levels-graphs.pdf)
10. [UPR Río Piedras mathematics department seminar abstract](https://math.uprrp.edu/seminarios/abstracts/dejter3.pdf)
11. [On invariants of extended 1-perfect codes, arXiv](https://arxiv.org/pdf/0903.5049)
12. [Italo J. Dejter, arXiv Combinatorics author listing](https://www.arxiv.symmetricfunctions.com/author/italo-j-dejter)
13. [arXiv 2403.05643 (Dejter, 2024)](https://arxiv.org/html/2403.05643)
14. [Ajc V42 P099.pdf, ajc.maths.uq.edu.au](https://ajc.maths.uq.edu.au/pdf/42/ajc_v42_p099.pdf)
---
*Topic: Encyclopedia › Physical world and mathematics › Physical and mathematical scientists › Mathematicians and statisticians › Logicians, set theorists, and combinatorialists › Graph theorists*
*Initially written Oct 10, 2026 · Edited: Oct 11, 2026; Oct 15, 2026*
*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*
License: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license