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INDONESIA
Indonesian Journal of Combinatorics
Published by Indonesian Combinatorial Society
ISSN : 25412205     EISSN : -     DOI : -
Core Subject : Science,
Computer Science & IT Decision Sciences, Operations Research & Management
Indonesian Journal of Combinatorics (IJC) publishes current research articles in any area of combinatorics and graph theory such as graph labelings, optimal network problems, metric dimension, graph coloring, rainbow connection and other related topics. IJC is published by the Indonesian Combinatorial Society (InaCombS), CGANT Research Group Universitas Jember (UNEJ), and Department of Mathematics Universitas Indonesia (UI).
Arjuna Subject : -
Articles 103 Documents
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The forcing monophonic and forcing geodetic numbers of a graph Johnson John
Indonesian Journal of Combinatorics Vol 4, No 2 (2020)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2020.4.2.5

Abstract

For a connected graph G = (V, E), let a set S be a m-set of G. A subset T ⊆ S is called a forcing subset for S if S is the unique m-set containing T. A forcing subset for S of minimum cardinality is a minimum forcing subset of S. The forcing monophonic number of S, denoted by fm(S), is the cardinality of a minimum forcing subset of S. The forcing monophonic number of G, denoted by fm(G), is fm(G) = min{fm(S)}, where the minimum is taken over all minimum monophonic sets in G. We know that m(G) ≤ g(G), where m(G) and g(G) are monophonic number and geodetic number of a connected graph G respectively. However there is no relationship between fm(G) and fg(G), where fg(G) is the forcing geodetic number of a connected graph G. We give a series of realization results for various possibilities of these four parameters.
Computing the split domination number of grid graphs V. R. Girish; P. Usha
Indonesian Journal of Combinatorics Vol 5, No 1 (2021)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2021.5.1.1

Abstract

A set D - V is a dominating set of G if every vertex in V - D is adjacent to some vertex in D. The dominating number γ(G) of G is the minimum cardinality of a dominating set D. A dominating set D of a graph G = (V;E) is a split dominating set if the induced graph (V - D) is disconnected. The split domination number γs(G) is the minimum cardinality of a split domination set. In this paper we have introduced a new method to obtain the split domination number of grid graphs by partitioning the vertex set in terms of star graphs and also we haveobtained the exact values of γs(Gm;n); m ≤ n; m,n ≤ 24:
Locating-chromatic number of the edge-amalgamation of trees Hilda Assiyatun; Dian Kastika Syofyan; Edy Tri Baskoro
Indonesian Journal of Combinatorics Vol 4, No 2 (2020)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2020.4.2.6

Abstract

The investigation on the locating-chromatic number for graphs was initially studied by Chartrand et al. on 2002. This concept is in fact a special case of the partition dimension for graphs. Even though this topic has received much attention, the current progress is still far from satisfaction. We can define the locating-chromatic number of a graph G as the smallest integer k such that there exists a proper k-coloring on the vertex-set of G such that all vertices have distinct coordinates (color codes) with respect to this coloring. Not like the metric dimension of any tree which is completely solved, the locating-chromatic number for most types of trees are still open. In this paper, we study the locating-chromatic number of trees. In particular, we give lower and upper bounds of the locating-chromatic number of trees formed by an edge-amalgamation of the collection of smaller trees. We also show that the bounds are tight.
Broader families of cordial graphs Christian Barrientos; Sarah Minion
Indonesian Journal of Combinatorics Vol 5, No 1 (2021)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2021.5.1.6

Abstract

A binary labeling of the vertices of a graph G is cordial if the number of vertices labeled 0 and the number of vertices labeled 1 differ by at most 1, and the number of edges of weight 0 and the number of edges of weight 1 differ by at most 1. In this paper we present general results involving the cordiality of graphs that results of some well-known operations such as the join, the corona, the one-point union, the splitting graph, and the super subdivision. In addition we show a family of cordial circulant graphs.
On the Locating Chromatic Number of Barbell Shadow Path Graph A. Asmiati; Maharani Damayanti; Lyra Yulianti
Indonesian Journal of Combinatorics Vol 5, No 2 (2021)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2021.5.2.4

Abstract

The locating-chromatic number was introduced by Chartrand in 2002. The locating chromatic number of a graph is a combined concept between the coloring and partition dimension of a graph. The locating chromatic number of a graph is defined as the cardinality of the minimum color classes of the graph. In this paper, we discuss about the locating-chromatic number of shadow path graph and barbell graph containing shadow graph.
Relationship between adjacency and distance matrix of graph of diameter two Siti L. Chasanah; Elvi Khairunnisa; Muhammad Yusuf; Kiki A. Sugeng
Indonesian Journal of Combinatorics Vol 5, No 2 (2021)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2021.5.2.1

Abstract

The relationship among every pair of vertices in a graph can be represented as a matrix, such as in adjacency matrix and distance matrix. Both adjacency and distance matrices have the same property. Adjacency and distance matrices are both symmetric matrix with diagonals entries equals to 0.  In this paper, we discuss relationships between adjacency matrix and distance matrix of a graph of diameter two, which is D=2(J-I)-A. From this relationship, we  also determine the value of the determinant matrix A+D and the upper bound of determinant of matrix D.
All unicyclic graphs of order n with locating-chromatic number n-3 Edy Tri Baskoro; Arfin Arfin
Indonesian Journal of Combinatorics Vol 5, No 2 (2021)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2021.5.2.3

Abstract

Characterizing all graphs having a certain locating-chromatic number is not an easy task. In this paper, we are going to pay attention on finding all unicyclic graphs of order n (⩾ 6) and having locating-chromatic number n-3.
Odd Harmonious Labeling of Pn ⊵ C4 and Pn ⊵ D2(C4) Sabrina Shena Sarasvati; Ikhsanul Halikin; Kristiana Wijaya
Indonesian Journal of Combinatorics Vol 5, No 2 (2021)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2021.5.2.5

Abstract

A graph G with q edges is said to be odd harmonious if there exists an injection f:V(G) → ℤ2q so that the induced function f*:E(G)→ {1,3,...,2q-1} defined by f*(uv)=f(u)+f(v) is a bijection.Here we show that graphs constructed by edge comb product of path Pn and cycle on four vertices C4 or shadow of cycle of order four D2(C4) are odd harmonious.
On local antimagic vertex coloring of corona products related to friendship and fan graph Zein Rasyid Himami; Denny Riama Silaban
Indonesian Journal of Combinatorics Vol 5, No 2 (2021)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2021.5.2.7

Abstract

Let G=(V,E) be connected graph. A bijection f : E → {1,2,3,..., |E|} is a local antimagic of G if any adjacent vertices u,v ∈ V satisfies w(u)≠ w(v), where w(u)=∑e∈E(u) f(e), E(u) is the set of edges incident to u. When vertex u is assigned the color w(u), we called it a local antimagic vertex coloring of G. A local antimagic chromatic number of G, denoted by χla(G), is the minimum number of colors taken over all colorings induced by the local antimagic labeling of G. In this paper, we determine the local antimagic chromatic number of corona product of friendship and fan with null graph on m vertices, namely, χla(Fn ⊙ \overline{K_m}) and χla(f(1,n) ⊙ \overline{K_m}).
The degree sequences of a graph with restrictions Rikio Ichishima; Francesc A. Muntaner-Batle; Miquel Rius-Font; Yukio Takahashi
Indonesian Journal of Combinatorics Vol 5, No 2 (2021)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2021.5.2.2

Abstract

Two finite sequences s1 and s2 of nonnegative integers are called bigraphical if there exists a bipartite graph G with partite sets V1 and V2 such that s1 and s2 are the degrees in G of the vertices in V1 and V2, respectively. In this paper, we introduce the concept of 1-graphical sequences and present a necessary and sufficient condition for a sequence to be 1-graphical in terms of bigraphical sequences.

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