PD-prime cordial labeling of graphs
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Abstract:
vspace{0.2cm} Let $G$ be a graph and $f:V(G)rightarrow {1,2,3,.....left|V(G)right|}$ be a bijection. Let $p_{uv}=f(u)f(v)$ and\ $ d_{uv}= begin{cases} left[frac{f(u)}{f(v)}right] ~~if~~ f(u) geq f(v)\ \ left[frac{f(v)}{f(u)}right] ~~if~~ f(v) geq f(u)\ end{cases} $\ for all edge $uv in E(G)$. For each edge $uv$ assign the label $1$ if $gcd (p_{uv}, d_{uv})=1$ or $0$ otherwise. $f$ is called PD-prime cordial labeling if $left|e_{f}left(0right)-e_{f}left(1right) right| leq 1$ where $e_{f}left(0right)$ and $e_{f}left(1right)$ respectively denote the number of edges labelled with $0$ and $1$. A graph with admit a PD-prime cordial labeling is called PD-prime cordial graph. & & vspace{0.2cm}
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Journal title
volume 51 issue 2
pages 1- 7
publication date 2019-12-01
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