Zata Yumni Awanis

@unram.ac.id

Department of Mathematics, Faculty of Mathematics and Natural Sciences
University of Mataram

Zata Yumni Awanis


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https://researchid.co/yumniawns

RESEARCH INTERESTS

Graph theory, graph coloring
14

Scopus Publications

Scopus Publications

  • The Strong 3-Rainbow Index of Graphs Containing some Cycles
    Zata Yumni Awanis, A. N. M. Salman, Suhadi Wido Saputro
    Journal of the Indonesian Mathematical Society, 2026
    A tree of minimum size in an edge-colored connected graph G is a rainbow Steiner tree if no two edges of G are colored the same. For an integer k, the strong k-rainbow index $srx_k(G)$ of G is the smallest number of colors required in an edge-coloring of G so that there exists a rainbow Steiner tree connecting every k-subset S of V(G). We focus on k=3. It is obvious that $srx_3(G)\\leq\\lVert G\\rVert$ where $\\lVert G\\rVert$ denotes the size of G. It has been proven that $srx_3(T_n)=\\lVert T_n\\rVert$. In this paper, we study how the $srx_3(T_n)$ changes when we add at least one edge to $T_n$. We provide a sharp upper bound and exact values of $srx_3(G)$ where G is a graph containing at most two cycles. We obtain that $srx_3(G)=\\lVert G\\rVert$ where G is a unicyclic graph of girth 7 or at least 9. Otherwise, $srx_3(G)<\\lVert G\\rVert$.
  • Strong rainbow vertex-connection number of comb product of a path and a connected graph
    Zata Yumni Awanis, I. Gede Adhitya Wisnu Wardhana, Irwansyah
    Aip Conference Proceedings, 2025
  • The Wiener Index, the Harmonic Index, and the Graph Representation of the Prime Ideal Graph for the Integers Modulo Rings with Prime Power Order
    Hindani Kusuma Ningrum, Evi Yuniartika Asmarani, I Gede Adhitya Wisnu Wardhana, Salwa, Zata Yumni Awanis
    Springer Proceedings in Mathematics and Statistics, 2024
  • THE POWER GRAPH REPRESENTATION FOR INTEGER MODULO GROUP WITH POWER PRIME ORDER
    Lalu Riski Wirendra Putra, Zata Yumni Awanis, Salwa Salwa, Qurratul Aini, I Gede Adhitya Wisnu Wardhana
    Barekeng, 2023
    There are many applications of graphs in various fields. Starting from chemical problems, such as the molecular shape of a compound to internet network problems, we can also use graphs to depict the abstract concept of a mathematical structure.. Groups in Algebra can be represented as a graph. This is interesting because Groups are abstract objects in mathematics. The graph of a group shows the physical form of the group by looking at the relationship between its elements. So, we can know the distance of the elements. In 2013, Abawajy et al. conducted studies related to power graphs. Power graph representation of groups of integers modulo with the order of prime numbers has been carried out in 2022 by Syechah, et al. In this article, the author provides the properties of a power graph on a group of integers modulo with the order of powers of prime numbers.
  • On the Locating Rainbow Connection Number of Trees and Regular Bipartite Graphs
    Ariestha W. Bustan, A. N. M. Salman, Pritta E. Putri, Zata Y. Awanis
    Emerging Science Journal, 2023
    Locating the rainbow connection number of graphs is a new mathematical concept that combines the concepts of the rainbow vertex coloring and the partition dimension. In this research, we determine the lower and upper bounds of the locating rainbow connection number of a graph and provide the characterization of graphs with the locating rainbow connection number equal to its upper and lower bounds to restrict the upper and lower bounds of the locating rainbow connection number of a graph. We also found the locating rainbow connection number of trees and regular bipartite graphs. The method used in this study is a deductive method that begins with a literature study related to relevant previous research concepts and results, making hypotheses, conducting proofs, and drawing conclusions. This research concludes that only path graphs with orders 2, 3, 4, and complete graphs have a locating rainbow connection number equal to 2 and the order of graph G, respectively. We also showed that the locating rainbow connection number of bipartite regular graphs is in the range of r-⌊n/4⌋+2 to n/2+1, and the locating rainbow connection number of a tree is determined based on the maximum number of pendants or the maximum number of internal vertices. Doi: 10.28991/ESJ-2023-07-04-016 Full Text: PDF
  • Modular Version of Edge Irregularity Strength for Fan and Wheel Graphs
    Debi Oktia Haryeni, Zata Yumni Awanis, Martin Bača, Andrea Semaničová-Feňovčíková
    Symmetry, 2022
    A k-labeling from the vertex set of a simple graph G=(V,E) to a set of integers {1,2,…,k} is defined to be a modular edge irregular if, for every couple of distinct edges, their modular edge weights are distinct. The modular edge weight is the remainder of the division of the sum of end vertex labels by modulo |E(G)|. The modular edge irregularity strength of a graph is known as the maximal vertex label k, minimized over all modular edge irregular k-labelings of the graph. In this paper we describe labeling schemes with symmetrical distribution of even and odd edge weights and investigate the existence of (modular) edge irregular labelings of joins of paths and cycles with isolated vertices. We estimate the bounds of the (modular) edge irregularity strength for the join graphs Pn+Km¯ and Cn+Km¯ and determine the corresponding exact value of the (modular) edge irregularity strength for some fan graphs and wheel graphs in order to prove the sharpness of the presented bounds.
  • THE INTERSECTION GRAPH REPRESENTATION OF A DIHEDRAL GROUP WITH PRIME ORDER AND ITS NUMERICAL INVARIANTS
    Dewi Santri Ramdani, I Gede Adhitya Wisnu Wardhana, Zatta Yumni Awanis
    Barekeng, 2022
    One of the concepts in mathematics that developing rapidly today is Graph Theory. The development of Graph Theory has been combined with Group Theory, that is by representing a group in a graph. The intersection graph from group , noted by , is a graph whose vertices are all non-trivial subgroups of group and two distinct vertices are adjacent in if and only if . In this research the intersection graph of a Dihedral group, we looking for the shapes and numerical invariants. The results obtained are if for , then has a subgraphs and subgraphs , the girth of the graph is 3, radius and diameter of the graph in a row is 2 and 3, and the chromatic number of the graph is
  • Graphs with strong 3-rainbow index equals 2
    A N M Salman, Z Y Awanis, S W Saputro
    Journal of Physics Conference Series, 2022
    Let G be an edge-colored connected graph of order n ≥ 3, where adjacent edges may be colored the same. Let k be an integer with 2 ≤ k ≤ n and S ⊆ V (G) with |S| = k. The Steiner distance d(S) of S is the minimum size of a tree in G connecting S. The strong k-rainbow index srxk (G) of G is the minimum number of colors required to color the edges of G so that every set S in G is connected by a tree of size d(S) whose edges have distinct colors. We focus on k = 3. In this paper, we first characterize the graphs G with srx 3 (G) = 2. According to the definition, it is clearly that ‖G‖ is the trivial upper bound for srx 3(G). Several previous researchers have shown that there exist some connected graphs G such that srx 3(G) = ‖G‖. Hence, in this paper, we provide another graph G such that srx 3(G) = ‖G‖.
  • THE STRONG 3-RAINBOW INDEX OF SOME CERTAIN GRAPHS AND ITS AMALGAMATION
    Zata Yumni Awanis, A.N.M. Salman
    Opuscula Mathematica, 2022
    We introduce a strong \\(k\\)-rainbow index of graphs as modification of well-known \\(k\\)-rainbow index of graphs. A tree in an edge-colored connected graph \\(G\\), where adjacent edge may be colored the same, is a rainbow tree if all of its edges have distinct colors. Let \\(k\\) be an integer with \\(2\\leq k\\leq n\\). The strong \\(k\\)-rainbow index of \\(G\\), denoted by \\(srx_k(G)\\), is the minimum number of colors needed in an edge-coloring of \\(G\\) so that every \\(k\\) vertices of \\(G\\) is connected by a rainbow tree with minimum size. We focus on \\(k=3\\). We determine the strong \\(3\\)-rainbow index of some certain graphs. We also provide a sharp upper bound for the strong \\(3\\)-rainbow index of amalgamation of graphs. Additionally, we determine the exact values of the strong \\(3\\)-rainbow index of amalgamation of some graphs.
  • The strong 3-rainbow index of edge-comb product of a path and a connected graph
    Zata Yumni Awanis, A.N.M. Salman, Suhadi Wido Saputro
    Electronic Journal of Graph Theory and Applications, 2022
    A tree in an edge-colored connected graph G is a rainbow tree if all of its edges have different colors. Let k be an integer with 2 ≤ k ≤ n and S be a k -subset of V ( G ) . The strong k -rainbow index srx k ( G ) of G is the smallest number of colors required in an edge-coloring of G such that every set S in G is connected by a rainbow tree with minimum size. In this paper, we investigate the srx 3 of edge-comb product of a path and a connected graph, denoted by P on (cid:3) (cid:126)e H . It is obvious that the natural upper bound for srx 3 ( P on (cid:3) (cid:126)e H ) is | E ( P on (cid:3) (cid:126)e H ) | . Hence, we first provide graphs H with srx 3 ( P on (cid:3) (cid:126)e H ) = | E ( P on (cid:3) (cid:126)e H ) | , then provide a sharper upper bound for srx 3 ( P on (cid:3) (cid:126)e H ) where srx 3 ( P on (cid:3) (cid:126)e H ) (cid:54) = | E ( P on (cid:3) (cid:126)e H ) | . We also provide the exact values of srx 3 ( P on (cid:3) (cid:126)e H ) for some graphs H .
  • Rainbow connection number of comb product of graphs
    Dinny Fitriani, ANM Salman, Zata Yumni Awanis
    Electronic Journal of Graph Theory and Applications, 2022
  • The strong 3-rainbow index of comb product of a tree and a connected graph
    Zata Yumni Awanis, A.N.M. Salman, Suhadi Wido Saputro
    Journal of Information Processing, 2020
  • The strong 3-rainbow index of edge-amalgamation of some graphs
    Z. Y. Awanis, A. Salman, S. Saputro, M. Bača, A. Semaničová-Feňovčíková
    Turkish Journal of Mathematics, 2020
  • The 3-rainbow index of amalgamation of some graphs with diameter 2
    Zata Yumni Awanis, A.N. M. Salman
    Journal of Physics Conference Series, 2019