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All Journal Journal of the Indonesian Mathematical Society Jurnal Matematika UNAND
Hilda Assiyatun, Hilda
Combinatorial Mathematics Research Group Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung
Computer Science & IT Mathematics

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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 Locating-Chromatic Numbers of Subdivisions of Friendship Graph Salindeho, Brilly Maxel; Assiyatun, Hilda; Baskoro, Edy Tri
Journal of the Indonesian Mathematical Society Volume 26 Number 2 (July 2020)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.26.2.822.175-184

Abstract

Let c be a k-coloring of a connected graph G and let pi={C1,C2,...,Ck} be the partition of V(G) induced by c. For every vertex v of G, let c_pi(v) be the coordinate of v relative to pi, that is c_pi(v)=(d(v,C1 ),d(v,C2 ),...,d(v,Ck )), where d(v,Ci )=min{d(v,x)|x in Ci }. If every two vertices of G have different coordinates relative to pi, then c is said to be a locating k-coloring of G. The locating-chromatic number of G, denoted by chi_L (G), is the least k such that there exists a locating k-coloring of G. In this paper, we determine the locating-chromatic numbers of some subdivisions of the friendship graph Fr_t, that is the graph obtained by joining t copies of 3-cycle with a common vertex, and we give lower bounds to the locating-chromatic numbers of few other subdivisions of Fr_t.
KARAKTERISASI POHON DENGAN BILANGAN DOMINASI-LOKASI-METRIK TIGA Zulfaneti, Zulfaneti; Baskoro, Edy Tri; Assiyatun, Hilda
Jurnal Matematika UNAND Vol 13, No 4 (2024)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.13.4.340-348.2024

Abstract

Misalkan G = (V;E) adalah graf sederhana dan terhubung. Untuk suatu himpunan R = fr1; r2; : : : ; rkg V dan v 2 V , representasi titik v terhadap R adalah vektor r(vjR) = (d(v; r1); d(v; r2); : : : ; d(v; rk)) dimana d(v; r) menyatakan jarak titik v dan titik r. Himpunan R disebut himpunan pembeda dari G jika semua titik di G memiliki representasi unik terhadap R. Himpunan D disebut himpunan dominasi dari G jikasetiap titik di G-D bertetangga dengan suatu titik v 2 D. Suatu himpunan dominasidan juga merupakan himpunan pembeda disebut himpunan dominasi-lokasi-metrik dariG. Kardinalitas dari himpunan dominasi-lokasi-metrik minimum dari G disebut bilangan dominasi-lokasi-metrik dari G. Semua graf orde n dengan bilangan dominasi-lokasi-metrik 1, 2, n-2 dan n-3 telah ditentukan secara lengkap. Dalam tulisan ini, kamimengkarakterisasi semua pohon dengan bilangan-dominasi-lokasi-metrik 3 dan secarakhusus membuktikan bahwa tidak ada pohon dengan bilangan-dominasi-lokasi-metriksama dengan dimensi metriknya.
KARAKTERISASI POHON DENGAN BILANGAN DOMINASI-LOKASI-METRIK TIGA Zulfaneti, Zulfaneti; Baskoro, Edy Tri; Assiyatun, Hilda
Jurnal Matematika UNAND Vol. 13 No. 4 (2024)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.13.4.340-348.2024

Abstract

Misalkan G = (V;E) adalah graf sederhana dan terhubung. Untuk suatu himpunan R = fr1; r2; : : : ; rkg V dan v 2 V , representasi titik v terhadap R adalah vektor r(vjR) = (d(v; r1); d(v; r2); : : : ; d(v; rk)) dimana d(v; r) menyatakan jarak titik v dan titik r. Himpunan R disebut himpunan pembeda dari G jika semua titik di G memiliki representasi unik terhadap R. Himpunan D disebut himpunan dominasi dari G jikasetiap titik di G-D bertetangga dengan suatu titik v 2 D. Suatu himpunan dominasidan juga merupakan himpunan pembeda disebut himpunan dominasi-lokasi-metrik dariG. Kardinalitas dari himpunan dominasi-lokasi-metrik minimum dari G disebut bilangan dominasi-lokasi-metrik dari G. Semua graf orde n dengan bilangan dominasi-lokasi-metrik 1, 2, n-2 dan n-3 telah ditentukan secara lengkap. Dalam tulisan ini, kamimengkarakterisasi semua pohon dengan bilangan-dominasi-lokasi-metrik 3 dan secarakhusus membuktikan bahwa tidak ada pohon dengan bilangan-dominasi-lokasi-metriksama dengan dimensi metriknya.
Characterization of \mathcal{R}(2K_2,F_n) with Minimum Order for Small n Fajri, Muhammad Rafif; Assiyatun, Hilda; Baskoro, Edy Tri
Journal of the Indonesian Mathematical Society Vol. 31 No. 2 (2025): JUNE
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i2.1871

Abstract

A Fan graph $F_n$ is defined as the graph $P_n+K_1$, where $P_n$ is the path on $n$ vertices. The notation $F \rightarrow (G, H)$ means that if all edges of $F$ are arbitrarily colored by red or blue, then either the subgraph of $F$ induced by all red edges contains a graph $G$ or the subgraph of $F$ induced by all blue edges contains a graph $H.$ Let $\mathcal{R}(G, H)$ denote the set of all graphs $F$ satisfying $F \rightarrow (G, H)$ and for every $e \in E(F),$ $(F - e) \not\rightarrow (G, H).$ In this paper, we propose some properties for a graph $G$ of minimum order that belongs to $\mathcal{R}(2K_2,F_n),$ for $n \geq 3$. We have also found all members of $\mathcal{R}(2K_2,F_n)$ with a minimum order for $n \in [3,7]$.
Co-Authors Edy Tri Baskoro Edy Tri Baskoro Fajri, Muhammad Rafif Rismawati Ramdani Salindeho, Brilly Maxel Salman, A.N.M Zulfaneti Zulfaneti