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All Journal Matematika: Jurnal Teori dan Terapan Journal of the Indonesian Mathematical Society Journal of Mathematical and Fundamental Sciences Kubik JURNAL ISTEK Indonesian Journal of Combinatorics KUBIK: Jurnal Publikasi Ilmiah Matematika
Rismawati Ramdani
Department Of Mathematics, Faculty Of Sciences And Technologies, Universitas Islam Negeri Sunan Gunung Djati, Jalan A.H. Nasution No. 105,
Astronomy Chemistry Computer Science & IT Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Mathematics Physics

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Journal : Journal of the Indonesian Mathematical Society

 1 
On The Total Edge and Vertex Irregularity Strength of Some Graphs Obtained from Star Ramdani, Rismawati; Salman, A.N.M; Assiyatun, Hilda
Journal of the Indonesian Mathematical Society Volume 25 Number 3 (November 2019)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.25.3.828.314-324

Abstract

Let $G=(V(G),E(G))$ be a graph and $k$ be a positive integer. A total $k$-labeling of $G$ is a map $f: V(G)\cup E(G)\rightarrow \{1,2,\ldots,k \}$. The edge weight $uv$ under the labeling $f$ is denoted by $w_f(uv)$ and defined by $w_f(uv)=f(u)+f(uv)+f(v)$. The vertex weight $v$ under the labeling $f$ is denoted by $w_f(v)$ and defined by $w_f(v) = f(v) + \sum_{uv \in{E(G)}} {f(uv)}$. A total $k$-labeling of $G$ is called an edge irregular total $k$-labeling of $G$ if  $w_f(e_1)\neq w_f(e_2)$ for every two distinct edges $e_1$ and $e_2$  in $E(G)$.  The total edge irregularity strength of $G$, denoted by $tes(G)$, is the minimum $k$ for which $G$ has an edge irregular total $k$-labeling.  A total $k$-labeling of $G$ is called a vertex irregular total $k$-labeling of $G$ if  $w_f(v_1)\neq w_f(v_2)$ for every two distinct vertices $v_1$ and $v_2$ in $V(G)$.  The total vertex irregularity strength of $G$, denoted by $tvs(G)$, is the minimum $k$ for which $G$ has a vertex irregular total $k$-labeling.  In this paper, we determine the total edge irregularity strength and the total vertex irregularity strength of some graphs obtained from star, which are gear, fungus, and some copies of stars.
On The Total Edge and Vertex Irregularity Strength of Some Graphs Obtained from Star Rismawati Ramdani; A.N.M Salman; Hilda Assiyatun
Journal of the Indonesian Mathematical Society Volume 25 Number 3 (November 2019)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.25.3.828.314-324

Abstract

Let $G=(V(G),E(G))$ be a graph and $k$ be a positive integer. A total $k$-labeling of $G$ is a map $f: V(G)\cup E(G)\rightarrow \{1,2,\ldots,k \}$. The edge weight $uv$ under the labeling $f$ is denoted by $w_f(uv)$ and defined by $w_f(uv)=f(u)+f(uv)+f(v)$. The vertex weight $v$ under the labeling $f$ is denoted by $w_f(v)$ and defined by $w_f(v) = f(v) + \sum_{uv \in{E(G)}} {f(uv)}$. A total $k$-labeling of $G$ is called an edge irregular total $k$-labeling of $G$ if  $w_f(e_1)\neq w_f(e_2)$ for every two distinct edges $e_1$ and $e_2$  in $E(G)$.  The total edge irregularity strength of $G$, denoted by $tes(G)$, is the minimum $k$ for which $G$ has an edge irregular total $k$-labeling.  A total $k$-labeling of $G$ is called a vertex irregular total $k$-labeling of $G$ if  $w_f(v_1)\neq w_f(v_2)$ for every two distinct vertices $v_1$ and $v_2$ in $V(G)$.  The total vertex irregularity strength of $G$, denoted by $tvs(G)$, is the minimum $k$ for which $G$ has a vertex irregular total $k$-labeling.  In this paper, we determine the total edge irregularity strength and the total vertex irregularity strength of some graphs obtained from star, which are gear, fungus, and some copies of stars.
Co-Authors A.N.M Salman A.N.M. Salman Arief Fatchul Huda Arief Fathcul Huda Asep Solih Awalluddin Desi Laswati Suwandi Esih Sukaesih Hilda Assiyatun Hilda Assiyatun Hilda Assiyatun, Hilda Nisa Nur Arafah Salman, A.N.M Selvi Marcelina