$4$-total mean cordial labeling of spider graph

	$4$-total mean cordial labeling of spider graph
Journal of Algorithms and Computation
مقاله 1، دوره 55، شماره 1، شهریور 2023، صفحه 1-9 اصل مقاله (271.8 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22059/jac.2023.92447
نویسندگان
R Ponraj^* ¹؛ S SUBBULAKSHMI²؛ Prof.Dr M.Sivakumar³
¹Department of Mathematics Sri Parakalyani College Alwarkurichi -627 412, India
²Sri Paramakalyani College Alwarkurichi-627412, Tamilnadu, India
³Head, Department of Mathematis Thiruvalluvar University College of Arts and Science Tittagudi Tamilnadu ,India
چکیده
Let $G$ be a graph. Let $f:V\left(G\right)\rightarrow \left\{0,1,2,\ldots,k-1\right\}$ be a function where $k\in \mathbb{N}$ and $k>1$. For each edge $uv$, assign the label $f\left(uv\right)=\left\lceil \frac{f\left(u\right)+f\left(v\right)}{2}\right\rceil$. $f$ is called a $k$-total mean cordial labeling of $G$ if $\left\|t_{mf}\left(i\right)-t_{mf}\left(j\right) \right\| \leq 1$, for all $i,j\in\left\{0,1,2,\ldots,k-1\right\}$, where $t_{mf}\left(x\right)$ denotes the total number of vertices and edges labelled with $x$, $x\in\left\{0,1,2,\ldots,k-1\right\}$. A graph with admit a $k$-total mean cordial labeling is called $k$-total mean cordial graph. In this paper we investigate the $4$-total mean cordial labeling behaviour of some spider graph.

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