The Compared Costs of Domination Location-Domination and Identification
Let = ( ) be a finite graph and ≥ 1 be an integer. For ∈ , let ) = { ∈ : ) ≤ } be the ball of radius centered at . A set ⊆ is an -dominating code if for all ∈ , we have ) ∩ ≠ ∅; it is an -locating-dominating code if for all ∈ , we have ) ∩ ≠ ∅, and for any two distinct non-codewords ∈ \ , ∈ \ , we h...
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| Published in | Discussiones Mathematicae. Graph Theory Vol. 40; no. 1; pp. 127 - 147 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Sciendo
01.01.2020
University of Zielona Góra |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1234-3099 2083-5892 2083-5892 |
| DOI | 10.7151/dmgt.2129 |
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| Summary: | Let
= (
) be a finite graph and
≥ 1 be an integer. For
∈
, let
) = {
∈
:
) ≤
} be the ball of radius
centered at
. A set
⊆
is an
-dominating code if for all
∈
, we have
) ∩
≠ ∅; it is an
-locating-dominating code if for all
∈
, we have
) ∩
≠ ∅, and for any two distinct non-codewords
∈
\
,
∈
\
, we have
) ∩
≠
) ∩
; it is an
-identifying code if for all
∈
, we have
) ∩
≠ ∅, and for any two distinct vertices
∈
,
∈
, we have
) ∩
≠
) ∩
. We denote by γ
) (respectively,
) and
)) the smallest possible cardinality of an
-dominating code (respectively, an
-locating-dominating code and an
-identifying code). We study how small and how large the three differences
)−
),
)−γ
) and
) − γ
) can be. |
|---|---|
| ISSN: | 1234-3099 2083-5892 2083-5892 |
| DOI: | 10.7151/dmgt.2129 |