A totally magic cordial labeling of one-point union of n copies of a graph
A graph \(G\) is said to have a totally magic cordial (TMC) labeling with constant \(C\) if there exists a mapping \(f: V(G)\cup E(G)\rightarrow \left\{0,1\right\}\) such that \(f(a) + f(b) + f(ab) \equiv C(\mbox{mod 2})\) for all \(ab\in E(G)\) and \(\left|n_f(0)-n_f(1)\right|\leq1\), where \(n_f(i...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AGH Univeristy of Science and Technology Press
2014-01-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | http://www.opuscula.agh.edu.pl/vol34/1/art/opuscula_math_3407.pdf |
| Summary: | A graph \(G\) is said to have a totally magic cordial (TMC) labeling with constant \(C\) if there exists a mapping \(f: V(G)\cup E(G)\rightarrow \left\{0,1\right\}\) such that \(f(a) + f(b) + f(ab) \equiv C(\mbox{mod 2})\) for all \(ab\in E(G)\) and \(\left|n_f(0)-n_f(1)\right|\leq1\), where \(n_f(i)\) \((i = 0, 1)\) is the sum of the number of vertices and edges with label \(i\). In this paper, we establish the totally magic cordial labeling of one-point union of \(n\)-copies of cycles, complete graphs and wheels. |
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| ISSN: | 1232-9274 |