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RAINBOW CONNECTION NUMBER AND TOTAL RAINBOW CONNECTION NUMBER OF AMALGAMATION RESULTS DIAMOND GRAPH(〖Br〗_4) AND FAN GRAPH(F_3)

BAREKENG: Jurnal Ilmu Matematika dan Terapan · Vol. 16 No. 1 (2022) · pp. 023–030

DOI
10.30598/barekengvol16iss1pp023-030
ISSN
2615-3017, 1978-7227
Published
2022-03-21
Publisher
PATTIMURA UNIVERSITY
Language
eng

Abstract

If be a graph and edge coloring of G is a function, rainbow connection number is the minimum-k coloration of the rainbow on the edge of graph G and denoted by rc(G). Rainbow connection numbers can be applied to the result of operations on some special graphs, such as diamond graphs and fan graphs. Graph operation is a method used to obtain a new graph by combining two graphs. This study performed amalgamation operations to obtain rainbow connection numbers and rainbow-total-connection numbers in diamond graphs ( ) and fan graphs ( ) or. Based on the research, it is obtained that the rainbow-connection number theorem on the amalgamation result of the diamond graph ( ) and fan graph ( is with. Furthermore, the theorem related to the total rainbow-connection number on the amalgamation result of the diamond graph( ) and the fan graph ( is obtained, namely with.

Collaboration network of the authors

16 authors · 42 co-authorship links

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  • Mulawarman University
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
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Co-authorOrganisationJoint articles
Nurwan NurwanAffiliation unknown2
Nisky Imansyah YahyaAffiliation unknown1
Ainun FatmawatiAffiliation unknown1
Muhammad Rezky Friesta PayuAffiliation unknown1
Djihad WungguliAffiliation unknown1
Jefri N. IsaAffiliation unknown1
Stella JunusAffiliation unknown1
Asyril AsyrilMulawarman University1
Nanda Arista RizkiAffiliation unknown1
Maulidah MaulidahAffiliation unknown1
Carolina Fadia DewiAffiliation unknown1
Dhira SyahlafandiAffiliation 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) 
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	<dc:title xml:lang="en-US">RAINBOW CONNECTION NUMBER AND TOTAL RAINBOW CONNECTION NUMBER OF AMALGAMATION RESULTS DIAMOND GRAPH(〖Br〗_4) AND FAN GRAPH(F_3)</dc:title>
	<dc:creator>Ismail, Sumarno</dc:creator>
	<dc:creator>Hasan, Isran K.</dc:creator>
	<dc:creator>Sigar, Tesya</dc:creator>
	<dc:creator>Nasib, Salmun K.</dc:creator>
	<dc:description xml:lang="en-US">If  be a graph and edge coloring of G is a function  , rainbow connection number is the minimum-k coloration of the rainbow on the edge of graph G and denoted by rc(G). Rainbow connection numbers can be applied to the result of operations on some special graphs, such as diamond graphs and fan graphs. Graph operation is a method used to obtain a new graph by combining two graphs. This study performed amalgamation operations to obtain rainbow connection numbers and rainbow-total-connection numbers in diamond graphs ( ) and fan graphs ( ) or  . Based on the research, it is obtained that the rainbow-connection number theorem on the amalgamation result of the diamond graph ( ) and fan graph ( &amp;nbsp;is  &amp;nbsp;with  . Furthermore, the theorem related to the total rainbow-connection number on the amalgamation result of the diamond graph( ) and the fan graph ( &amp;nbsp;is obtained, namely  &amp;nbsp;with  .</dc:description>
	<dc:publisher xml:lang="en-US">PATTIMURA UNIVERSITY</dc:publisher>
	<dc:date>2022-03-21</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/4027</dc:identifier>
	<dc:identifier>10.30598/barekengvol16iss1pp023-030</dc:identifier>
	<dc:source xml:lang="en-US">BAREKENG: Jurnal Ilmu Matematika dan Terapan; Vol 16 No 1 (2022): BAREKENG: Jurnal Ilmu Matematika dan Terapan; 023-030</dc:source>
	<dc:source>2615-3017</dc:source>
	<dc:source>1978-7227</dc:source>
	<dc:source>10.30598/barekengvol16iss1year2022</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/4027/3999</dc:relation>
</oai_dc:dc>