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Yang, Hong; Rashid, Muhammad Aamer; Ahmad, Sarfraz; Siddiqui, Muhammad Kamran; Hanif, Muhammad Farhan

Cycle super magic labeling of pumpkin, octagonal and hexagonal graphs. (English) Zbl 1495.05311

J. Discrete Math. Sci. Cryptography 22, No. 7, 1165-1176 (2019).
Summary: A simple graph \(G(V, E)\) admits an \(H\)-covering, if every edge in \(E(G)\) belongs to a subgraph of \(G\) isomorphic to \(H\). The graph \(G\) is said to be \(H\)-magic, if there exists a bijection \(\psi : V(G) \cup E(G) \rightarrow \{1, 2, 3, \dots, |V(G)|+|E(G)|\}\) such that for every subgraph \(H^\prime\) of \(G\) isomorphic to \(H\), \(\sum\limits_{v\in V(H^\prime)}\psi(v)+\sum\limits_{v\in E(H^\prime)}\psi(e)\) is constant. Moreover \(G\) is said to be \(H\)-super magic, if \(\psi (V(G)) = \{1, 2, 3, \dots, |V(G)|\}\). In this paper, we study the cycle-super magic labeling of a pumpkin graph and two classes of planar maps containing 8-sided and 4-sided faces or 6-sided and 4-sided faces, respectively.

Cited in 6 Documents

MSC:

05C78 Graph labelling (graceful graphs, bandwidth, etc.)

Keywords:

total labeling; edge-covering; cycle-super magic labeling

Software:

NISPOC
Cite Review PDF
Full Text: DOI

References:

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