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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In this paper, we present results for middle graphs of path and cycle and some splitting graphs of path and cycle on double edge-vertex domination numbers.
📌 3 Key Takeaways
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Objective & Hypothesis:An edge $e=uv$ of graph $G=(V,E)$ is said to be edge-vertex dominate vertices $u$ and $v$, as well as all vertices adjacent to $u$ and $v$.
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Key Findings & Data:A set $S \subseteq E $ is a double edge-vertex dominating set if every vertex of $V$ is edge-vertex dominated by at least two edges of $S$.
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Conclusion & Impact:In this paper, we present results for middle graphs of path and cycle and some splitting graphs of path and cycle on double edge-vertex domination numbers.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Double edge-vertex dominating set · Double vertex-edge dominating set · Edge-vertex dominating set
Abstract
An edge $e=uv$ of graph $G=(V,E)$ is said to be edge-vertex dominate vertices $u$ and $v$, as well as all vertices adjacent to $u$ and $v$. A set $S \subseteq E $ is a double edge-vertex dominating set if every vertex of $V$ is edge-vertex dominated by at least two edges of $S$. The minimum cardinality of a double edge-vertex dominating set of $G$ is the double edge-vertex domination number and is denoted by $\gamma_{dev}(G)$. In this paper, we present results for middle graphs of path and cycle and some splitting graphs of path and cycle on double edge-vertex domination numbers.
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Cite This Article
AYLI, B., KILIC, E. (2021). Double Edge-Vertex Domination on Middle and Splitting Graphs of Path and Cycle. Fundamental Journal of Mathematics and Applications, Cilt: 4 Sayı: 4, 221–231. https://ajindex.com/articles/905681