Variants of the domination number for flower snarks

Burdett, Ryan; Haythorpe, Michael; Newcombe, Alex

doi:10.26493/1855-3974.2710.f3d

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2024

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Cited by 3 publications

References 32 publications

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Computation of Captive, Half Certified and Majority Domination Numbers of a Family of 3-Regular Graphs

Kalaiselvi,

Venkatraman

2024

Lecture Notes in Networks and Systems

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Computation of Captive, Half Certified and Majority Domination Numbers of a Family of 3-Regular Graphs

Kalaiselvi,

Venkatraman

2024

Lecture Notes in Networks and Systems

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A Cross-Entropy Approach to the Domination Problem and Its Variants

Burdett,

Haythorpe,

Newcombe

2024

Entropy

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The domination problem and three of its variants (total domination, 2-domination, and secure domination) are considered. These problems have various real-world applications, including error correction codes, ad hoc routing for wireless networks, and social network analysis, among others. However, each of them is NP-hard to solve to provable optimality, making fast heuristics for these problems desirable. There are a wealth of highly developed heuristics and approximation algorithms for the domination problem; however, such heuristics are much less common for variants of the domination problem. We redress this gap in the literature by proposing a novel implementation of the cross-entropy method that can be applied to any sensible variant of domination. We present results from experiments that demonstrate that this approach can produce good results in an efficient manner even for larger graphs and that it works roughly as well for any of the domination variants considered.

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Optimizing SNARK networks via double metric dimension

Ahmad,

Faheem,

Bajri

et al. 2024

MATH

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<p>Doubly resolving sets (DRSs) provide a promising approach for source detection. They consist of minimal subsets of nodes with the smallest cardinality, referred to as the double metric dimension (DMD), that can uniquely identify the location of any other node within the network. Utilizing DRSs can improve the accuracy and efficiency of the identification of the origin of a diffusion process. This ability is crucial for early intervention and control in scenarios such as epidemic outbreaks, misinformation spreading in social media, and fault detection in communication networks. In this study, we computed the DMD of flower snarks $ J_{m} $ and quasi-flower snarks $ G_{m} $ by describing their minimal doubly resolving sets (MDRSs). We deduce that the DMD for the flower snarks $ J_{m} $ is finite and depends on the network's order, and the DMD for the quasi-flower snarks $ G_{m} $ is finite and independent of the network's order. Furthermore, our findings offer valuable insights into the structural features of complex networks. This knowledge can offer direction for future studies in network theory and its practical implementations.</p>

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Variants of the domination number for flower snarks

Cited by 3 publications

References 32 publications

Computation of Captive, Half Certified and Majority Domination Numbers of a Family of 3-Regular Graphs

Computation of Captive, Half Certified and Majority Domination Numbers of a Family of 3-Regular Graphs

A Cross-Entropy Approach to the Domination Problem and Its Variants

Optimizing SNARK networks via double metric dimension

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