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All Journal KADIKMA Jurnal Daya Matematis UNEJ e-Proceeding BAREKENG: Jurnal Ilmu Matematika dan Terapan JPKMI (Jurnal Pengabdian Kepada Masyarakat Indonesia) Jurnal Ilmu Pendidikan Sekolah Dasar CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS

Rafiantika Megahnia Prihandini

Program Studi Pendidikan Matematika, Universitas Jember, Indonesia

Author-ID : 5286193

Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Energy Engineering Environmental Science Mathematics Mechanical Engineering Physics Public Health Social Sciences Transportation Other

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Pewarnaan Titik Ketakteraturan Lokal Refleksif pada Keluarga Graf Tangga Rizki Aulia Akbar; Dafik Dafik; Rafiantika Megahnia Prihandini
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 3, No 1 (2022): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Let a simple and connected graph $G=(V,E)$ with the vertex set $V(G)$ and the edge set E(G). If there is a mapping $f$: $V(G)$ $\rightarrow$ ${0,2,…,2k_v}$ and $f$: $E(G)$ $\rightarrow$ ${1,2,…,k_e}$ as a function of vertex and edge irregularities labeling with $k=max$ ${2k_v,k_e}$ for $k_v$ and $k_e$ natural numbers and the associated weight of vertex $u,v \in V(G)$ under $f$ is $w(u)=f(u)+\sum_{u,v\in E(G)}f(uv)$. Then the function $f$ is called a local vertex irregular reflexive labeling if every adjacent vertices has distinct vertex weight. When each vertex of graph $G$ is colored with a vertex weight $w(u,v)$, then graph $G$ is said to have a local vertex irregular reflexive coloring. Minimum number of vertex weight is needed to color the vertices in graf $G$ such that any adjacent vertices are not have the same color is called a local vertex irregular reflexive chromatic number, denoted by $\chi_{(lrvs)}(G)$. The minimum $k$ required such that $\chi_{(lrvs)}(G)=\chi(G)$ where $\chi(G)$ is chromatic number of proper coloring on G is called local reflexive vertex color strength, denoted by $lrvcs(G)$. In this paper, we will examine the local reflexive vertex color strength of local vertex irregular reflexive coloring on the family of ladder graph.

Dimensi Metrik Ketetanggaan Lokal pada Graf Hasil Operasi Korona G odot P_3 dan G odot S_4 Alfin Nabila Taufik; Dafik Dafik; Rafiantika Megahnia Prihandini; Ridho Alfarisi
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 2 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

There are variant of the metric dimensions in graph theory, one of them is a local adjacency metric dimension. Let $W\subset V(G)$ with $W=\{w_1,w_2,\dots,w_k\}$, the representation of the vertex $V\in V(G)$, $r_A(v|W)=(d_A(v,w_1),d_A(v,w_2),\dots,d_A(v,w_k))$ with $ d_ {A} (v, w) $= $ 0 $ if $ v = w $, $ d_ {A} (v, w) $= $ 1 $ if $ v$ adjacent to $w $, and $ d_ {A} (v, w) $ =$ 2 $ if $ v $ does not adjacent to $ w $. If every two adjacent vertices $ v_1 $, $ v_2 \in V (G) $, $ r_ {A} (v_1 | W) \neq r_ {A} (v_2 | W) $, then $W$ is the minimum cardinality of the local adjacency metric dimension. The minimum cardinality of $W$ is called the local adjacency metric dimension number, denoted by $ \dim_{(A, l)} (G) $. In this paper, we have found the local adjacency metric dimension of corona product of special graphs, namely the $ L_n \odot {P_3} $ graph, $ S_n \odot {P_3} $ graph, $ C_n \odot {P_3} $ graph, $ P_n \odot {S_4} $ graph, and the graph $ L_n \odot {S_4} $.

Rainbow Vertex Antimagic Coloring 2-Connection paada Keluarga Graf Tangga Ahmad Musyaffa' Hikamuddin; Dafik Dafik; Rafiantika Megahnia Prihandini
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 3, No 2 (2022): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25037/cgantjma.v3i2.88

All graph in this paper are connected graph and simple graph. Let G = (V,E)be a connected graph. Rainbow vertex connection is the assignment of G that has interior vertices with different colors. The minimum number of colors from the rainbow vertex coloring in graph G is called rainbow vertex connection number. If wf(u) ̸= wf(v) for two different vertext u, v ∈ V (G) then f is called antimagic labeling for graph G. Rainbow vertex antimagic coloring is a combination between rainbow coloring and antimagic labeling. Graph G is called rainbow vertex antimagic coloring 2-connection if G has at least 2 rainbow paths from u − v. Rainbow vertex antimagic coloring 2-connection to denoted as rvac2(G). In this paper, we will study rainbow vertex antimagic coloring 2-connection on a family of graphs ladder that includes H-graph Hn for n ≥ 2, slide ladder graph SLn for n ≥ 2, and graph Octa-Chain OCn for n ≥ 2.

Co-Authors Ahmad Musyaffa' Hikamuddin Alfin Nabila Taufik Anis Nur Afni Arika Indah Kristiana Bea Hana Siswati D. Dafik Deddy Setyawan Ermita Rizki Albirri Ika Hesti Agustin, Ika Hesti Jamhari Jamhari Ridho Alfarisi Rizki Aulia Akbar Robiatul Adawiyah Susi Setiawani

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