# Leaps: an approach to the block structure of a graph

Henry Martyn Mulder; Ladislav Nebeský

Discussiones Mathematicae Graph Theory (2006)

- Volume: 26, Issue: 1, page 77-90
- ISSN: 2083-5892

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topHenry Martyn Mulder, and Ladislav Nebeský. "Leaps: an approach to the block structure of a graph." Discussiones Mathematicae Graph Theory 26.1 (2006): 77-90. <http://eudml.org/doc/270237>.

@article{HenryMartynMulder2006,

abstract = {To study the block structure of a connected graph G = (V,E), we introduce two algebraic approaches that reflect this structure: a binary operation + called a leap operation and a ternary relation L called a leap system, both on a finite, nonempty set V. These algebraic structures are easily studied by considering their underlying graphs, which turn out to be block graphs. Conversely, we define the operation $+_G$ as well as the set of leaps $L_G$ of the connected graph G. The underlying graph of $+_G$, as well as that of $L_G$, turns out to be just the block closure of G (i.e., the graph obtained by making each block of G into a complete subgraph).},

author = {Henry Martyn Mulder, Ladislav Nebeský},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {leap; leap operation; block; cut-vertex; block closure; block graph},

language = {eng},

number = {1},

pages = {77-90},

title = {Leaps: an approach to the block structure of a graph},

url = {http://eudml.org/doc/270237},

volume = {26},

year = {2006},

}

TY - JOUR

AU - Henry Martyn Mulder

AU - Ladislav Nebeský

TI - Leaps: an approach to the block structure of a graph

JO - Discussiones Mathematicae Graph Theory

PY - 2006

VL - 26

IS - 1

SP - 77

EP - 90

AB - To study the block structure of a connected graph G = (V,E), we introduce two algebraic approaches that reflect this structure: a binary operation + called a leap operation and a ternary relation L called a leap system, both on a finite, nonempty set V. These algebraic structures are easily studied by considering their underlying graphs, which turn out to be block graphs. Conversely, we define the operation $+_G$ as well as the set of leaps $L_G$ of the connected graph G. The underlying graph of $+_G$, as well as that of $L_G$, turns out to be just the block closure of G (i.e., the graph obtained by making each block of G into a complete subgraph).

LA - eng

KW - leap; leap operation; block; cut-vertex; block closure; block graph

UR - http://eudml.org/doc/270237

ER -

## References

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- [2] F. Harary, A characterization of block graphs, Canad. Math. Bull. 6 (1963) 1-6, doi: 10.4153/CMB-1963-001-x. Zbl0112.25002
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