Leaps: an approach to the block structure of a graph

• Autorzy: Henry Martyn Mulder , Ladislav Nebeský
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

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

Kategorie tematyczne

• 05C75: Structural characterization of families of graphs
• 05C99: None of the above, but in this section
• 08A99: None of the above, but in this section

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2006
• Tom: 26
• Numer: 1
• Strony: 77-90

Daty

wydano

2006

otrzymano

2005-01-14

poprawiono

2005-06-20

Twórcy

autor

Henry Martyn Mulder

• Econometrisch Instituut, Erasmus Universiteit, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands

autor

Ladislav Nebeský

• Filozofická Fakulta, Univerzita Karlova v Praze, J. Palacha 2, 116 38 Praha 1, Czech Republic

Bibliografia

• [1] M. Changat, S. Klavžar and H.M. Mulder, The all-path transit function of a graph, Czechoslovak Math. J. 51 (2001) 439-448, doi: 10.1023/A:1013715518448.
• [2] F. Harary, A characterization of block graphs, Canad. Math. Bull. 6 (1963) 1-6, doi: 10.4153/CMB-1963-001-x.
• [3] F. Harary, Graph Theory (Addison-Wesley, Reading MA, 1969).
• [4] M.A. Morgana and H.M. Mulder, The induced path convexity, betweenness, and svelte graphs, Discrete Math. 254 (2002) 349-370, doi: 10.1016/S0012-365X(01)00296-5.
• [5] H.M. Mulder, The interval function of a graph (MC-tract 132, Mathematish Centrum, Amsterdam 1980).
• [6] H.M. Mulder, Transit functions on graphs, in preparation.
• [7] L. Nebeský, A characterization of the interval function of a graph, Czechoslovak Math. J. 44 (119) (1994) 173-178.
• [8] L. Nebeský, Geodesics and steps in a connected graph, Czechoslovak Math. J. 47 (122) (1997) 149-161.
• [9] L. Nebeský, An algebraic characterization of geodetic graphs, Czechoslovak Math. J. 48 (123) (1998) 701-710.
• [10] L. Nebeský, A tree as a finite nonempty set with a binary operation, Mathematica Bohemica 125 (2000) 455-458.
• [11] L. Nebeský, New proof of a characterization of geodetic graphs, Czechoslovak Math. J. 52 (127) (2002) 33-39.

Identyfikatory

DOI

10.7151/dmgt.1303