This research paper focuses on creating a Python module to analyze the Minkowski-4 Mean Cordial Labeling characteristics in various graph types, specifically Path, Cycle, Wheel, Star, and W \( _{n}\) P \( _{m}\) graphs. A graph G \(=\) (p,q) with p vertices and q edges is said to have a Minkowski-4 Mean Cordial Labeling if there exists f:V(G) \({\rightarrow }\{0,1,2\}\) such that for each edge \(e = (u,v)\) , the label is determined by the Minkowski-4 Mean Cordial Labeling of the labels of its two end-points u and v. Minkowski-4 Mean Cordial Labeling Formula is Mean Cordial Labeling of the labels of its two endpoints u and v: \(\begin{aligned} f^*(u,v)=\left\lceil {\left( \frac{{f\left( u\right) }^4+{f\left( v\right) }^4}{\textrm{2}}\right) }^{\mathrm {1/4}}\right\rceil \end{aligned}\) The function f is referred to as a Minkowski-4 Mean Cordial labeling if the conditions \(\left| v_{f}(i) - v_{f}(j)\right| \le 1\) and \(\left| e_{f}(i) - e_{f}(j)\right| \le 1\) for \(i,j \in \{0,1,2\}\) , where v \( _{f}(x)\) and e \( _{f}(x)\) represent the number of edges and vertices respectively, labeled with x ( \(x = 0, 1, 2\) ) while researchers have extensively explored Minkowski-4 Mean Labeling across various graphs, the concept Minkowski-4 Mean Cordial Labeling has not been investigated. The study seeks to address this gap by focusing on the application of Minkowski-4 mean cordial labeling to different types of graphs, aiming to enhance the existing body of knowledge in this area. This research can contribute to machine learning and AI research.

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Minkowski-4 Mean Cordial Labeling Characteristics in Various Graphs

  • C. Muthulakshmi Sasikala,
  • A. Akil Nivetha

摘要

This research paper focuses on creating a Python module to analyze the Minkowski-4 Mean Cordial Labeling characteristics in various graph types, specifically Path, Cycle, Wheel, Star, and W \( _{n}\) P \( _{m}\) graphs. A graph G \(=\) (p,q) with p vertices and q edges is said to have a Minkowski-4 Mean Cordial Labeling if there exists f:V(G) \({\rightarrow }\{0,1,2\}\) such that for each edge \(e = (u,v)\) , the label is determined by the Minkowski-4 Mean Cordial Labeling of the labels of its two end-points u and v. Minkowski-4 Mean Cordial Labeling Formula is Mean Cordial Labeling of the labels of its two endpoints u and v: \(\begin{aligned} f^*(u,v)=\left\lceil {\left( \frac{{f\left( u\right) }^4+{f\left( v\right) }^4}{\textrm{2}}\right) }^{\mathrm {1/4}}\right\rceil \end{aligned}\) The function f is referred to as a Minkowski-4 Mean Cordial labeling if the conditions \(\left| v_{f}(i) - v_{f}(j)\right| \le 1\) and \(\left| e_{f}(i) - e_{f}(j)\right| \le 1\) for \(i,j \in \{0,1,2\}\) , where v \( _{f}(x)\) and e \( _{f}(x)\) represent the number of edges and vertices respectively, labeled with x ( \(x = 0, 1, 2\) ) while researchers have extensively explored Minkowski-4 Mean Labeling across various graphs, the concept Minkowski-4 Mean Cordial Labeling has not been investigated. The study seeks to address this gap by focusing on the application of Minkowski-4 mean cordial labeling to different types of graphs, aiming to enhance the existing body of knowledge in this area. This research can contribute to machine learning and AI research.