The differential and the Roman domination number of a graph

S Bermudo, H Fernau, JM Sigarreta - Applicable Analysis and Discrete …, 2014 - JSTOR
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 …

[HTML][HTML] Computing the differential of a graph: hardness, approximability and exact algorithms

S Bermudo, H Fernau - Discrete Applied Mathematics, 2014 - Elsevier
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 …

[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 …

[HTML][HTML] Combinatorics for smaller kernels: The differential of a graph

S Bermudo, H Fernau - Theoretical Computer Science, 2015 - 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 D is defined as∂(D)=| B (D)|−| D| and …

[HTML][HTML] 1-well-covered graphs revisited

VE Levit, E Mandrescu - European Journal of Combinatorics, 2019 - Elsevier
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 …

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 …

[PDF][PDF] Relations between the differential and parameters in graphs

S Bermudo, JC Hernández, JM Rodrıguez… - Organizadas por el …, 2014 - webs-deim.urv.cat
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 …

[HTML][HTML] Data reductions and combinatorial bounds for improved approximation algorithms

FN Abu-Khzam, C Bazgan, M Chopin… - Journal of Computer and …, 2016 - Elsevier
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 …

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 …

β-Differential of a Graph

LA Basilio, S Bermudo, J Leaños, JM Sigarreta - Symmetry, 2017 - mdpi.com
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 …