A Gallai-type equality for the total domination number of a graph

• Autorzy: Sanming Zhou
• Języki publikacji: EN

Abstrakty

EN

We prove the following Gallai-type equality
γₜ(G) + εₜ(G) = p
for any graph G with no isolated vertex, where p is the number of vertices of G, γₜ(G) is the total domination number of G, and εₜ(G) is the maximum integer s such that there exists a spanning forest F with s the number of pendant edges of F minus the number of star components of F.

Słowa kluczowe

EN

domination number; total domination number; Gallai equality

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2004
• Tom: 24
• Numer: 3
• Strony: 539-543

Daty

wydano

2004

otrzymano

2003-10-09

poprawiono

2004-04-14

Twórcy

autor

Sanming Zhou

• Department of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia

Bibliografia

• [1] B. Bollobás, E.J. Cockayne and C.M. Mynhardt, On Generalized Minimal Domination Parameters for Paths, Discrete Math. 86 (1990) 89-97, doi: 10.1016/0012-365X(90)90352-I.
• [2] E.J. Cockayne, S.T. Hedetniemi and R. Laskar, Gallai Theorems for Graphs, Hypergraphs and Set Systems, Discrete Math. 72 (1988) 35-47, doi: 10.1016/0012-365X(88)90192-6.
• [3] T. Gallai, Über Extreme Punkt-und Kantenmengen, Ann. Univ. Sci. Budapest Eötvös Sect. Math. 2 (1959) 133-138.
• [4] S.T. Hedetniemi, Hereditary Properties of Graphs, J. Combin. Theory 14 (1973) 16-27.
• [5] S.T. Hedetniemi and R. Laskar, Connected Domination in Graphs, in: B. Bollobás ed., Graph Theory and Combinatorics (Academic Press, 1984) 209-218.
• [6] J. Nieminen, Two Bounds for the Domination Number of a Graph, J. Inst. Math. Appl. 14 (1974) 183-187, doi: 10.1093/imamat/14.2.183.

Identyfikatory

DOI

10.7151/dmgt.1251