Geodesic
Domination numbers on the Boolean function graph of a graph
Mathematica Bohemica, Tome 130 (2005) no. 2, pp. 135-151.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

For any graph $G$, let $V(G)$ and $E(G)$ denote the vertex set and the edge set of $G$ respectively. The Boolean function graph $B(G, L(G), \mathop {\mathrm NINC})$ of $G$ is a graph with vertex set $V(G)\cup E(G)$ and two vertices in $B(G, L(G), \mathop {\mathrm NINC})$ are adjacent if and only if they correspond to two adjacent vertices of $G$, two adjacent edges of $G$ or to a vertex and an edge not incident to it in $G$. For brevity, this graph is denoted by $B_{1}(G)$. In this paper, we determine domination number, independent, connected, total, cycle, point-set, restrained, split and non-split domination numbers of $B_{1}(G)$ and obtain bounds for the above numbers.
DOI : 10.21136/MB.2005.134129
Classification : 05C15, 05C45, 05C69, 06E30
Keywords: domination number; point-set domination number; split domination number; Boolean function graph 
@article{10_21136_MB_2005_134129,
     author = {Janakiraman, T. N. and Muthammai, S. and Bhanumathi, M.},
     title = {Domination numbers on the {Boolean} function graph of a graph},
     journal = {Mathematica Bohemica},
     pages = {135--151},
     publisher = {mathdoc},
     volume = {130},
     number = {2},
     year = {2005},
     doi = {10.21136/MB.2005.134129},
     mrnumber = {2148647},
     zbl = {1110.05078},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2005.134129/}
}
TY  - JOUR
AU  - Janakiraman, T. N.
AU  - Muthammai, S.
AU  - Bhanumathi, M.
TI  - Domination numbers on the Boolean function graph of a graph
JO  - Mathematica Bohemica
PY  - 2005
SP  - 135
EP  - 151
VL  - 130
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2005.134129/
DO  - 10.21136/MB.2005.134129
LA  - en
ID  - 10_21136_MB_2005_134129
ER  - 
%0 Journal Article
%A Janakiraman, T. N.
%A Muthammai, S.
%A Bhanumathi, M.
%T Domination numbers on the Boolean function graph of a graph
%J Mathematica Bohemica
%D 2005
%P 135-151
%V 130
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2005.134129/
%R 10.21136/MB.2005.134129
%G en
%F 10_21136_MB_2005_134129
Janakiraman, T. N.; Muthammai, S.; Bhanumathi, M. Domination numbers on the Boolean function graph of a graph. Mathematica Bohemica, Tome 130 (2005) no. 2, pp. 135-151. doi : 10.21136/MB.2005.134129. http://geodesic.mathdoc.fr/articles/10.21136/MB.2005.134129/

Cité par Sources :