Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dominating and Irredundant Broadcasts in Graphs   A broadcast on a nontrivial connected graph G=(V,E) is a function f from V(G)
to {0,1,...,diam(G)} such that f(v) does not exceed the eccentricity of v. The
cost of f is the sum of the function values. A broadcast f is dominating if
each vertex of G is at distance at most f(v) from a vertex v with positive
f(v).
  We use properties of minimal dominating broadcasts to define the concept of
an irredundant broadcast on G. We determine conditions under which an
irredundant broadcast is maximal irredundant. Denoting the minimum costs of
dominating and maximal irredundant broadcasts by gamma_{b}(G) and ir_{b}(G)
respectively, the definitions imply that ir_{b}(G) is bounded above by
gamma_{b}(G) for all graphs. We show that gamma_{b} in turn is bounded above by
(5/4)ir_{b}(G) for all graphs G.
  We also briefly consider the upper broadcast number Gamma_{b}(G) and upper
irredundant broadcast number IR_{b}(G), and illustrate that the ratio IR_{b} to
Gamma_{b} is unbounded for general graphs.

25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph