2,562 research outputs found
The domination number of on-line social networks and random geometric graphs
We consider the domination number for on-line social networks, both in a
stochastic network model, and for real-world, networked data. Asymptotic
sublinear bounds are rigorously derived for the domination number of graphs
generated by the memoryless geometric protean random graph model. We establish
sublinear bounds for the domination number of graphs in the Facebook 100 data
set, and these bounds are well-correlated with those predicted by the
stochastic model. In addition, we derive the asymptotic value of the domination
number in classical random geometric graphs
Nordhaus-Gaddum bounds for locating domination
A dominating set S of graph G is called metric-locating-dominating if it is
also locating, that is, if every vertex v is uniquely determined by its vector
of distances to the vertices in S. If moreover, every vertex v not in S is also
uniquely determined by the set of neighbors of v belonging to S, then it is
said to be locating-dominating. Locating, metric-locating-dominating and
locating-dominating sets of minimum cardinality are called b-codes, e-codes and
l-codes, respectively. A Nordhaus-Gaddum bound is a tight lower or upper bound
on the sum or product of a parameter of a graph G and its complement G. In this
paper, we present some Nordhaus-Gaddum bounds for the location number b, the
metric-location-number e and the location-domination number l. Moreover, in
each case, the graph family attaining the corresponding bound is characterized.Comment: 7 pages, 2 figure
On global location-domination in graphs
A dominating set of a graph is called locating-dominating, LD-set for
short, if every vertex not in is uniquely determined by the set of
neighbors of belonging to . Locating-dominating sets of minimum
cardinality are called -codes and the cardinality of an LD-code is the
location-domination number . An LD-set of a graph is global
if it is an LD-set of both and its complement . The global
location-domination number is the minimum cardinality of a
global LD-set of . In this work, we give some relations between
locating-dominating sets and the location-domination number in a graph and its
complement.Comment: 15 pages: 2 tables; 8 figures; 20 reference
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