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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Prosiding Seminar Matematika dan Pendidikan Matematik UNEJ e-Proceeding Mathvision : Jurnal Matematika EIGEN MATHEMATICS JOURNAL Journal Focus Action of Research Mathematic (Factor M) Journal of Applied Statistics, Mathematics, and Data Science
Dwi Agustin Retnowardani
Universitas PGRI Argopuro Jember
Computer Science & IT Decision Sciences, Operations Research & Management Education Mathematics Other

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Journal : Journal Focus Action of Research Mathematic (Factor M)

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On the RACN of the comb product of the cycle C_3 with path P_n and broom Br_(n,m) Septory, Brian Juned; Retnowardani, Dwi Agustin; Dliou, Kamal
Journal Focus Action of Research Mathematic (Factor M) Vol. 8 No. 1 (2025): Vol. 8 No. 1 (2025)
Publisher : Universitas Islam Negeri (UIN) Syekh Wasil Kediri

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30762/f_m.v8i1.4755

Abstract

The combination of rainbow coloring and anti-magic labeling is known as Rainbow Antimagic Coloring (RAC). The Rainbow Antimagic Connection Number (RACN) of a graph G is the smallest number of colors induced by all edge weights under an antimagic labeling, symbolized as rac(G) A graph is said to have rainbow antimagic connectivity if for every pir of vetices x∈V(G), there exits a rainbow antimagic path, wherin all edge weights along the path are distinct. Let G be a graph with vertex set V(G) and edge set E(G). A bijective function f from V(G) to {1,2,…,|V(G)|} is applied, wherein the weight of the edge uv∈E(G) is defined as w(uv) under f which is obtained from w(xv)=f(x)+f(v). A rainbow path x-v is a path in a vertex-labeled graph G if for any two edges xv,x' v'∈E(P) the path satisfies w(xv)≠w(x'v'). If there is a rainbow x-v path P for every two vertices x,v∈V(G) then the function f is called a rainbow antimagic labeling of G. A graph G we say has an RAC, if we assign each edge xv with an edge weight color w(xv). In this paper, we present the RACN of the comb product of cycle C_3 with path P_n and broom Br_(n,m) symbolized by C_3⊳ P_n and C_3⊳Br_(n,m). A comb operation on a graph G, symbolized as G⊳H, is a graph product wherein each vertex of G is replaced by a copy of H, maintaining the structure of G. This operation helps construct new classes of graphs with specific connectivity and labeling properties.
Co-Authors Achmadin, Wahyu Nur Adinda Putri Aziza Alivia, Fitriatul Antonius Cahya Prihandoko Arika I. Kristiana Arika Indah Kristiana Audia Dwi Retno Wulandari D. Dafik Dewi Mashitasari Dliou, Kamal Fita Fatimah Fita Fatimah, Fita Ghozi, Mochammad Ali HARIADI, WIGID Hasanah, Laeliyatul Ika Hesti Agustin, Ika Hesti Indah Noor Dwi Kusuma Dewi Kamal Dliou Kamal Dliou Kamal, Dliou Kette, Efraim Kurniawan Dairo Kumanireng, Albert Mario Kusuma Dewi, Indah Noor Dwi Mashitasari, Dewi Masruroh, Zuwidatul Miftahur Roifah Ro'ifah, Miftahur Septory, Brian Juned Sulantari Wahyu Nur Achmadin Wigid Hariadi Wulandari, Audia Dwi Retno