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2023•Indian Journal of Science and TechnologyOpen access

Fuzzy Quotient -3 Cordial Labeling on Generalized Petersen Graph

P Sumathi, J Suresh Kumar

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Abstract

Objectives: To analyze the existence of fuzzy quotient-3 cordial labeling on the generalized Petersen graph. Methods: The method involves mathematically defining how to label the vertex of a generalized Petersen graph and demonstrating that these formulations produce fuzzy quotient-3 cordial labeling. Findings: In this study, we proved that the generalized Petersen graph GP(h;m) ; 1  m < ⌊ h 2 ⌋ is fuzzy quotient-3 cordial, except for h  0( mod 6). Novelty: Here, we give fuzzy quotient-3 cordial labeling to some families of graphs, namely Durer graph, Desargues graph, Dodecahedral graph, Mobius Kantor graph, Petersen graph, Cubical graph, Cubic symmetric graph, Nauru graph and the generalized Petersen graph GP(h;m) . Keywords: Labeling; Fuzzy Quotient -3 Cordial; Petersen Graph; Generalized Petersen Graph; Mobius Kantor Graph

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Objectives: To analyze the existence of fuzzy quotient-3 cordial labeling on the generalized Petersen graph. Methods: The method involves mathematically defining how to label the vertex of a generalized Petersen graph and demonstrating that these formulations produce fuzzy quotient-3 cordial labeling. Findings: In this study, we proved that the generalized Petersen graph GP(h;m) ; 1  m < ⌊ h 2 ⌋ is fuzzy quotient-3 cordial, except for h  0( mod 6). Novelty: Here, we give fuzzy quotient-3 cordial labeling to some families of graphs, namely Durer graph, Desargues graph, Dodecahedral graph, Mobius Kantor graph, Petersen graph, Cubical graph, Cubic symmetric graph, Nauru graph and the generalized Petersen graph GP(h;m) . Keywords: Labeling; Fuzzy Quotient -3 Cordial; Petersen Graph; Generalized Petersen Graph; Mobius Kantor Graph

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Available abstract

Objectives: To analyze the existence of fuzzy quotient-3 cordial labeling on the generalized Petersen graph. Methods: The method involves mathematically defining how to label the vertex of a generalized Petersen graph and demonstrating that these formulations produce fuzzy quotient-3 cordial labeling. Findings: In this study, we proved that the generalized Petersen graph GP(h;m) ; 1  m < ⌊ h 2 ⌋ is fuzzy quotient-3 cordial, except for h  0( mod 6). Novelty: Here, we give fuzzy quotient-3 cordial labeling to some families of graphs, namely Durer graph, Desargues graph, Dodecahedral graph, Mobius Kantor graph, Petersen graph, Cubical graph, Cubic symmetric graph, Nauru graph and the generalized Petersen graph GP(h;m) . Keywords: Labeling; Fuzzy Quotient -3 Cordial; Petersen Graph; Generalized Petersen Graph; Mobius Kantor Graph

Key concepts: Petersen graph, Combinatorics, Mathematics, Voltage graph, Distance-regular graph, Quotient, Discrete mathematics, Regular graph

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