TY - JOUR
ID - 69046
TI - $Z_k$-Magic Labeling of Some Families of Graphs
JO - Journal of Algorithms and Computation
JA - JAC
LA - en
SN - 2476-2776
AU - Jeyanthi, P.
AU - Jeyadaisy, K.
AD - Principal and Head of the Research Centre,Department of Mathematics,Govindammal Aditanar College for Women,Tiruchendur,Tamilnadu,INDIA
AD - Department of Mathematics
Holy Cross College, Nagercoil, Tamilnadu, India.
Y1 - 2018
PY - 2018
VL - 50
IS - issue 2
SP - 1
EP - 12
KW - A-magic labeling
KW - $Z_k$-magic labeling
KW - $Z_k$-magic graph
KW - total graph
KW - flower graph
KW - generalized prism graph
KW - closed helm graph
KW - lotus inside a circle graph
KW - $Godotoverline{K_m}$
KW - $m$-splitting graph
KW - $m$-shadow graph
DO - 10.22059/jac.2018.69046
N2 - For any non-trivial abelian group A under addition a graph $G$ is said to be $A$-\textit{magic} if there exists a labeling $f:E(G) \rightarrow A-\{0\}$ such that, the vertex labeling $f^+$ defined as $f^+(v) = \sum f(uv)$ taken over all edges $uv$ incident at $v$ is a constant. An $A$-\textit{magic} graph $G$ is said to be $Z_k$-magic graph if the group $A$ is $Z_k$ the group of integers modulo $k$. These $Z_k$-magic graphs are referred to as $k$-\textit{magic} graphs. In this paper we prove that the total graph, flower graph, generalized prism graph, closed helm graph, lotus inside a circle graph, $G\odot\overline{K_m}$, $m$-splitting graph of a path and $m$-shadow graph of a path are $Z_k$-magic graphs.
UR - https://jac.ut.ac.ir/article_69046.html
L1 - https://jac.ut.ac.ir/article_69046_6280f6ffe52fb49581c3603a8b60a45f.pdf
ER -