On the total $(k,r)$-domination number of random graphs

Author name not available (Why is that?)

Publication date: 23 November 2015

Abstract: A subset

S

of a vertex set of a graph

G

is a total

(k, r)

-dominating set if every vertex

u i n V (G)

is within distance

k

of at least

r

vertices in

S

. The minimum cardinality among all total

(k, r)

-dominating sets of

G

is called the total

(k, r)

-domination number of

G

, denoted by

g a m m a_{(k, r)}^{t} (G)

. We previously gave an upper bound on

g a m m a_{(2, r)}^{t} (G (n, p))

in random graphs with non-fixed

p i n (0, 1)

. In this paper we generalize this result to give an upper bound on

g a m m a_{(k, r)}^{t} (G (n, p))

in random graphs with non-fixed

p i n (0, 1)

for

k g e q 3

as well as present an upper bound on

g a m m a_{(k, r)}^{t} (G)

in graphs with large girth.

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