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Open access Jurnal SINTA 3

DIGRUNDY NUMBER OF DIRECTED STAR, BANANA TREE, FIREWORKS, AND COCONUT TREE GRAPHS

BAREKENG: Jurnal Ilmu Matematika dan Terapan · Vol. 20 No. 4 (2026) · pp. 3213–3222

DOI
10.30598/barekengvol20iss4pp3213-3222
ISSN
2615-3017, 1978-7227
Published
2026-08-24
Publisher
PATTIMURA UNIVERSITY
Language
eng
License
creativecommons.org/licenses/by-sa/4.0

Abstract

A digrundy coloring of a graph is a vertex coloring in which every vertex assigned a higher color is adjacent to vertices assigned all smaller colors. The maximum number of colors that can be realized in such a coloring of an acyclic directed graph is called the digrundy number. This paper determines the digrundy numbers of several classes of acyclic directed graphs, namely directed star graphs, directed banana tree graphs, directed fireworks graphs, and directed coconut tree graphs. The analysis is based on structural properties of the graphs and combinatorial arguments derived from digrundy coloring constraints. The results show that the digrundy number of directed star graphs is under orientations where the central vertex satisfies and. For directed banana tree graphs with a specified orientation, the digrundy number is for and for. Under arbitrary orientations, directed fireworks graphs have digrundy number, while for directed coconut tree graphs, the digrundy number is bounded by These findings provide exact values of the digrundy number for the graph classes considered and highlight the role of structural constraints in governing digrundy coloring behavior.

Collaboration network of the authors

8 authors · 14 co-authorship links

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Co-authorOrganisationJoint articles
Josua JosuaAffiliation unknown1
Evi NovianiAffiliation unknown1
Yundari YundariAffiliation unknown1
Nur'ainul Miftahul HudaAffiliation unknown1
Lisa FikadilaAffiliation unknown1
Fauziah SafitriAffiliation unknown1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://ojs3.unpatti.ac.id/index.php/barekeng/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.
Original metadata (oai_dc) 
<oai_dc:dc xmlns="http://www.openarchives.org/OAI/2.0/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/  http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
	<dc:title xml:lang="en-US">DIGRUNDY NUMBER OF DIRECTED STAR, BANANA TREE, FIREWORKS, AND COCONUT TREE GRAPHS</dc:title>
	<dc:creator>Raventino, Raventino</dc:creator>
	<dc:creator>Fran, Fransiskus</dc:creator>
	<dc:description xml:lang="en-US">A digrundy coloring of a graph is a vertex coloring in which every vertex assigned a higher color is adjacent to vertices assigned all smaller colors. The maximum number of colors that can be realized in such a coloring of an acyclic directed graph is called the digrundy number. This paper determines the digrundy numbers of several classes of acyclic directed graphs, namely directed star graphs, directed banana tree graphs, directed fireworks graphs, and directed coconut tree graphs. The analysis is based on structural properties of the graphs and combinatorial arguments derived from digrundy coloring constraints. The results show that the digrundy number of directed star graphs  &amp;nbsp;is  &amp;nbsp;under orientations where the central vertex satisfies  &amp;nbsp;and  . For directed banana tree graphs  &amp;nbsp;with a specified orientation  , the digrundy number is  &amp;nbsp;for  &amp;nbsp;and  &amp;nbsp;for  . Under arbitrary orientations, directed fireworks graphs  &amp;nbsp;have digrundy number  , while for directed coconut tree graphs  , the digrundy number is bounded by  &amp;nbsp;These findings provide exact values of the digrundy number for the graph classes considered and highlight the role of structural constraints in governing digrundy coloring behavior.</dc:description>
	<dc:publisher xml:lang="en-US">PATTIMURA UNIVERSITY</dc:publisher>
	<dc:date>2026-08-24</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/22242</dc:identifier>
	<dc:identifier>10.30598/barekengvol20iss4pp3213-3222</dc:identifier>
	<dc:source xml:lang="en-US">BAREKENG: Jurnal Ilmu Matematika dan Terapan; Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application; 3213-3222</dc:source>
	<dc:source>2615-3017</dc:source>
	<dc:source>1978-7227</dc:source>
	<dc:source>10.30598/barekengvol20iss4year2026</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/22242/13133</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2026 Raventino Raventino, Fransiskus Fran</dc:rights>
	<dc:rights xml:lang="en-US">http://creativecommons.org/licenses/by-sa/4.0</dc:rights>
</oai_dc:dc>