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The differential and the Roman domination number of a graph
Let G=(V, E) be a graph of order n and let B (S) be the set of vertices in V\S that have a
neighbor in the vertex set S. The differential of a vertex set S is defined as∂(S)=| B (S)|—| S …
neighbor in the vertex set S. The differential of a vertex set S is defined as∂(S)=| B (S)|—| S …
[HTML][HTML] Computing the differential of a graph: hardness, approximability and exact algorithms
We are studying computational complexity aspects of the differential of a graph, a graph
parameter previously introduced to model ways of influencing a network. We obtain NP …
parameter previously introduced to model ways of influencing a network. We obtain NP …
[HTML][HTML] On the differential and Roman domination number of a graph with minimum degree two
S Bermudo - Discrete Applied Mathematics, 2017 - Elsevier
Abstract Let G=(V, E) be a graph of order n and let B (D) be the set of vertices in V∖ D that
have a neighbor in the vertex set D. The differential of a vertex set D is defined as∂(D)=| B …
have a neighbor in the vertex set D. The differential of a vertex set D is defined as∂(D)=| B …
[HTML][HTML] Combinatorics for smaller kernels: The differential of a graph
Abstract Let G=(V, E) be a graph of order n and let B (D) be the set of vertices in V∖ D that
have a neighbor in the vertex set D. The differential of D is defined as∂(D)=| B (D)|−| D| and …
have a neighbor in the vertex set D. The differential of D is defined as∂(D)=| B (D)|−| D| and …
[HTML][HTML] 1-well-covered graphs revisited
A graph is well-covered if all its maximal independent sets are of the same size (Plummer,
1970). A well-covered graph is 1-well-covered if the deletion of any one vertex leaves a …
1970). A well-covered graph is 1-well-covered if the deletion of any one vertex leaves a …
The differential of the strong product graphs
S Bermudo, L De la Torre… - … Journal of Computer …, 2015 - Taylor & Francis
Let G=(V, E) be a graph of order n and let B (D) be the set of vertices in V∖ D that have a
neighbour in the set D. The differential of a set D is defined as∂(D)=| B (D)|−| D| and the …
neighbour in the set D. The differential of a set D is defined as∂(D)=| B (D)|−| D| and the …
[PDF][PDF] Relations between the differential and parameters in graphs
In this work, we obtain several tight bounds for the differential of a graph. In particular, we
relate the differential of a graph with known parameters of a graph, namely, its order, size …
relate the differential of a graph with known parameters of a graph, namely, its order, size …
[HTML][HTML] Data reductions and combinatorial bounds for improved approximation algorithms
Kernelization algorithms in the context of Parameterized Complexity are often based on a
combination of data reduction rules and combinatorial insights. We will expose in this paper …
combination of data reduction rules and combinatorial insights. We will expose in this paper …
The Metric Differential: An Efficient Approach for a Navigating Agent to Rapidly Locate Itself in a Graph Space Through Optimal Landmarks
N Ahmad, M Salman, F Ali - Arabian Journal for Science and Engineering, 2025 - Springer
In a connected graph space G (a discrete structure/a point space), the navigation of an AI
agent (assumed to be a point robot) can be taken into place with the help of fewest …
agent (assumed to be a point robot) can be taken into place with the help of fewest …
β-Differential of a Graph
Let G=(V, E) be a simple graph with vertex set V and edge set E. Let D be a subset of V, and
let B (D) be the set of neighbours of D in V∖ D. The differential∂(D) of D is defined as| B …
let B (D) be the set of neighbours of D in V∖ D. The differential∂(D) of D is defined as| B …