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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan
Prabhu, S
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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PMC-LABELING OF SOME CLASSES OF GRAPHS CONTAINING CYCLES Ponraj, R; Prabhu, S; Sivakumar, M
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss2pp1445-1456

Abstract

Let be a graph with p vertices and q edges. We have introduced a new graph labeling method using integers and cordial-related works and investigated some graphs for this labeling technique. Using this labeling concept, we have examined the graphs like path, cycle, star, complete graph, comb, and wheel graph. The first research paper on graph theory was published by Leonhard Euler. However, he did not use the word ‘graph’ in his work. In the early stages of the development of the subject, the vertices of a graph were specified as , and the edges were denoted by, . In recent times, several researchers have attempted to provide different types of labeling to the vertices and edges of a graph by identifying the relevant mathematical properties. The present paper provides a novel method of labeling by employing integers, which may form a foundation for future research work. In this paper, we investigate the pair mean cordial labeling behavior of some cycle-related graphs like the ice cream graph, closed web graph, circulant graph, zig-zag chord graph, pentagonal circular ladder, djembe graph, quadrilateral friendship graph, and origami graph.
PAIR MEAN CORDIAL LABELING OF HURDLE, KEY, LOTUS, AND NECKLACE GRAPHS Ponraj, R; Prabhu, S
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 4 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss4pp2795-2804

Abstract

Let be a graph with vertices and edges. Define and . Consider a mapping by assigning different labels in to the different elements of when is even and different labels in to elements of V and repeating a label for the remaining one vertex when is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge of G, there exists a labeling if is even and if is odd such that | |≤1 where and respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G for which there is a pair mean cordial labeling is called pair mean cordial graph(PMC-graph). In this paper, we investigate the pair mean cordial labeling of some graphs like hurdle graph, lotus graph, necklace graph, F-tree, Y-tree, subdivided shell graph, uniform bow graph and key graph.
Co-Authors Ponraj, R Sivakumar, M