Article Per Year (5 Year)
p-Index From 2021 - 2026
0.659
P-Index
This Author published in this journals
All Journal BIMASTER Journal of the Indonesian Mathematical Society Zero : Jurnal Sains, Matematika, dan Terapan
Raventino Raventino
Universitas Tanjungpura
Agriculture, Biological Sciences & Forestry Chemistry Decision Sciences, Operations Research & Management Mathematics Physics

Published : 3 Documents Claim Missing Document
Claim Missing Document
Check
Articles

Found 3 Documents
Search

 1 
BILANGAN DIACHROMATIC PADA GRAF BINTANG Raventino Raventino; Nilamsari Kusumastuti; Fransiskus Fran
Bimaster : Buletin Ilmiah Matematika, Statistika dan Terapannya Vol 10, No 3 (2021): Bimaster : Buletin Ilmiah Matematika, Statistika dan Terapannya
Publisher : FMIPA Universitas Tanjungpura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26418/bbimst.v10i3.47401

Abstract

Pewarnaan lengkap pada suatu graf G adalah pewarnaan titik dengan syarat setiap pasangan warna muncul minimal satu kali pada G. Maksimum banyaknya warna yang digunakan pada pewarnaan lengkap suatu graf tidak berarah G yang dinotasikan dengan ψ(G) disebut bilangan achromatic. Pada penelitian ini dibahas perluasan dari bilangan achromatic yaitu bilangan diachromatic, khususnya bilangan diachromatic graf bintang berarah K1,n. Graf bintang K1,n adalah graf yang memuat satu titik pusat yang berderajat n dan bertetangga dengan n daun. Bilangan diachromatic yang dinotasikan dengan dac(G), adalah maksimum banyaknya warna yang digunakan pada pewarnaan lengkap suatu graf berarah G. Pada penelitian ini diperoleh bahwa banyaknya warna (dinotasikan w) yang dapat digunakan dalam pewarnaan lengkap graf berarah G adalah bilangan bulat yang memenuhi permutasi  dari w (P2w) yang tidak lebih dari atau sama dengan banyaknya sisi di graf G. Selain itu didapat bahwa bilangan diachromatic pada graf bintang berarah K1,n  adalah dac(K1,n ) = 2.Kata Kunci: pewarnaan titik, pewarnaan lengkap, maksimum banyaknya warna.
Diachromatic Number of Some Acyclic Digraphs Raventino, Raventino; Susanti, Yeni
Journal of the Indonesian Mathematical Society Vol. 31 No. 3 (2025): SEPTEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i3.1710

Abstract

A vertex coloring that ensures every pair of different colors is represented at least once is termed complete coloring. The diachromatic number of an acyclic digraph denotes the maximum number of colors required for its complete coloring. This study delves into the diachromatic numbers of lobster digraphs, fireworks digraphs, banana tree digraphs, and coconut tree digraphs under specific and arbitrary directional orientations.
Exploring the Metric Chromatic Number of Uniform, Centralized Uniform, and Cycle Uniform Theta Graphs Raventino Raventino; Fransiskus Fran
ZERO: Jurnal Sains, Matematika dan Terapan Vol 10, No 1 (2026): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v10i1.27103

Abstract

Metric coloring allows adjacent vertices of a graph to share the same color provided that their associated distance vectors are distinct, leading to the concept of the metric chromatic number. This notion is closely related to problems of vertex distinguishability and resource allocation in network-like structures. In this paper, we present the first exact determination of the metric chromatic number for three families of theta type graphs: uniform theta graphs, centralized uniform theta graphs, and a newly introduced class called the cycle uniform theta graph, obtained by cyclically arranging uniform theta subgraphs. The proposed construction enables an investigation of how cyclic configurations influence metric coloring behavior. Using a constructive metric coloring approach, exact values of the metric chromatic number are obtained. It is shown that the uniform theta graph  and the centralized uniform theta graph  both satisfy  for all positive integers  and . For the cycle uniform theta graph , the metric chromatic number equals  when  and  have the same parity or when  is odd and  is even. In contrast,  when  is even and  is odd. This latter case arises because the longest path in the cyclic structure has odd length, forcing the graph to have chromatic number three. Since the graph is connected and its chromatic number is at most three, this structural constraint directly implies that three colors are also necessary for a valid metric coloring.
Co-Authors Fransiskus Fran Nilamsari Kusumastuti Yeni Susanti