CYCLE SUPER MAGIC LABELING
OF PLANAR GRAPHS
Bin Yang1, Muhammad Aamer Rashid2,
Sarfraz Ahmad2, Muhammad Faisal Nadeem2,
Muhammad Kamran Siddiqui3
1 School of Artificial Intelligence and Big Data
Hefei University, Hefei 230601, CHINA
2Department of Mathematics
COMSATS University Islamabad
Lahore Campus, 54000, PAKISTAN
3 Department of Mathematics
COMSATS University Islamabad
Lahore Campus, 54000, PAKISTAN

Abstract

A simple graph $G(V,E)$ admits a $H$-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 $\psi : V (G)\cup E(G) \rightarrow \{1, 2, 3, \dots , \vert V (G)\vert+\vert E(G)\vert\}$ such that for every subgraph $H'$ of $G$ isomorphic to $H$,
$\sum\limits_{v\in V(H')}\psi(v)+ \sum\limits_{e\in E(H')}\psi(e)$ is constant. Moreover $G$ is said to be $H$-supermagic, if $\psi(V (G)) = \{1, 2, 3, \dots , \vert V (G)\vert\}$. In this paper, we study the cycle-supermagic 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.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 32
Issue: 6
Year: 2019

DOI: 10.12732/ijam.v32i6.4

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