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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 75 Documents
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Structure of intersection graphs Haval M. Mohammed Salih; Sanaa M. S. Omer
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.2021.5.2.6

Abstract

 Let G be a finite group and let N be a fixed normal subgroup of G.  In this paper, a new kind of graph on G, namely the intersection graph is defined and studied. We use  to denote this graph, with its vertices are all normal subgroups of G and two distinct vertices are adjacent if their intersection in N. We show some properties of this graph. For instance, the intersection graph is a simple connected with diameter at most two. Furthermore we give the graph structure of  for some finite groups such as the symmetric, dihedral, special linear group, quaternion and cyclic groups. 
The complete short proof of the Berge conjecture Ikorong Anouk
Indonesian Journal of Combinatorics Vol 6, No 1 (2022)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2022.6.1.1

Abstract

We say that a graph B is berge if every graph B' ∈ {B,B̄} does not contain an induced cycle of odd length ≥ 5 [B̄ is the complementary graph of B}.A graph G is perfect if every induced subgraph G' of G satisfies χ(G')=ω(G'), where χ(G') is the chromatic number of G' and ω(G') is the clique number of G'. The Berge conjecture states that a graph H is perfect if and only if H is berge. Indeed, the Berge problem (or the difficult part of the Berge conjecture) consists to show that χ(B)=ω(B) for every berge graph B. In this paper, we give the direct short proof of the Berge conjecture by reducing the Berge problem into a simple equation of three unknowns and by using trivial complex calculus coupled with elementary computation and a trivial reformulation of that problem via the reasoning by reduction to absurd [we recall that the Berge conjecture was first proved by Chudnovsky, Robertson, Seymour and Thomas in a paper of at least 143 pages long. That being said, the new proof given in this paper is far more easy and more short].Our work in this paper is original and is completely different from all strong investigations made by Chudnovsky, Robertson, Seymour and Thomas in their manuscript of at least 143 pages long.
Prime ideal graphs of commutative rings Haval Mohammed Salih; Asaad A. Jund
Indonesian Journal of Combinatorics Vol 6, No 1 (2022)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2022.6.1.2

Abstract

Let R be a finite commutative ring with identity and P be a prime ideal of R. The vertex set is R - {0} and two distinct vertices are adjacent if their product in P. This graph is called the prime ideal graph of R and denoted by ΓP. The relationship among prime ideal, zero-divisor, nilpotent and unit graphs are studied. Also, we show that ΓP is simple connected graph with diameter less than or equal to two and both the clique number and the chromatic number of the graph are equal. Furthermore, it has girth 3 if it contains a cycle. In addition, we compute the number of edges of this graph and investigate some properties of ΓP.
The local metric dimension of split and unicyclic graphs Dinny Fitriani; Anisa Rarasati; Suhadi Wido Saputro; Edy Tri Baskoro
Indonesian Journal of Combinatorics Vol 6, No 1 (2022)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2022.6.1.3

Abstract

A set W is called a local resolving set of G if the distance of u and v to some elements of W are distinct for every two adjacent vertices u and v in G.  The local metric dimension of G is the minimum cardinality of a local resolving set of G.  A connected graph G is called a split graph if V(G) can be partitioned into two subsets V1 and V2 where an induced subgraph of G by V1 and V2 is a complete graph and an independent set, respectively.  We also consider a graph, namely the unicyclic graph which is a connected graph containing exactly one cycle.  In this paper, we provide a general sharp bounds of local metric dimension of split graph.  We also determine an exact value of local metric dimension of any unicyclic graphs.
On graphs with α- and b-edge consecutive edge magic labelings Christian Barrientos
Indonesian Journal of Combinatorics Vol 6, No 1 (2022)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2022.6.1.4

Abstract

Among the most studied graph labelings we have the varieties called alpha and edge-magic. Even when their definitions seem completely different, these labelings are related. A graceful labeling of a bipartite graph is called an α-labeling if the smaller labels are assigned to vertices of the same stable set. An edge-magic labeling of a graph of size n is said to be b-edge consecutive when its edges are labeled with the integers b+1, b+2, ..., b+n, for some 0 ≤ b ≤ n. In this work, we prove the existence of several b edge-magic labelings for any graph of order m and size m-1 that admits an α-labeling. In addition, we determine the exact value of b induced by the α-labeling, as well as for its reverse, complementary, and reverse complementary labelings.
Eigenvalues of antiadjacency matrix of Cayley graph of Z_n Juan Daniel; Kiki Ariyanti Sugeng; Nora Hariadi
Indonesian Journal of Combinatorics Vol 6, No 1 (2022)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2022.6.1.5

Abstract

In this paper, we give a relation between the eigenvalues of the antiadjacency matrix of Cay(Z_n, S) and the eigenvalues of the antiadjacency matrix of Cay(Z_n, (Z_n−{0})−S), as well as the eigenvalues of the adjacency matrix of Cay(Z_n, S). Then, we give the characterization of connection set S where the eigenvalues of the antiadjacency matrix of Cay(Z_n, S) are all integers.
On the number of caterpillars Christian Barrientos
Indonesian Journal of Combinatorics Vol 6, No 2 (2022)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2022.6.2.1

Abstract

A caterpillar is a tree obtained from a path by attaching pendant vertices. The number of caterpillars of size n is a well-known result. In this work extend this result exploring the number of caterpillars of size n together with the cardinalities of the stable sets and the diameter. Three closed formulas are presented, giving the number of caterpillars of size n with: (i) smaller stable set of cardinality k, (ii) diameter d, and (iii) diameter d and smaller stable set of cardinality k.
Index graphs of finite permutation groups Haval Mohammed Salih
Indonesian Journal of Combinatorics Vol 6, No 2 (2022)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2022.6.2.2

Abstract

Let G be a subgroup of Sn. For x ∈ G, the index of x in G is denoted by ind x is the minimal number of 2-cycles needed to express x as a product. In this paper, we define a new kind of graph on G, namely the index graph and denoted by Γind(G). Its vertex set the set of all conjugacy classes of G and two distinct vertices x ∈ Cx and y ∈ Cy are adjacent if Gcd(ind x, ind y) 6 ≠ 1. We study some properties of this graph for the symmetric groups Sn, the alternating group An, the cyclic group Cn, the dihedral group D2n and the generalized quaternain group Q4n. In particular, we are interested in the connectedness of them.
Hamming index of graphs with respect to its incidence matrix Harishchandra S. Ramane; Ishwar B. Baidari; Raju B. Jummannaver; Vinayak V. Manjalapur; Gouramma A. Gudodagi; Ashwini S. Yalnaik; Ajith S. Hanagawadimath
Indonesian Journal of Combinatorics Vol 6, No 2 (2022)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2022.6.2.4

Abstract

Let B(G) be the incidence matrix of a graph G. The row in B(G)corresponding to a vertex v, denoted by s(v) is the string which belongs to ℤm2, a set of m-tuples over a field of order two. The Hamming distance between the strings s(u) and s(v) is the number of positions in which s(u) and s(v) differ. In this paper we obtain the Hamming distance between the strings generated by the incidence matrix of a graph. The sum of Hamming distances between all pairs of strings, called Hamming index of a graph is obtained.
The total vertex irregularity strength of symmetric cubic graphs of the Foster's Census Rika Yanti; Gregory Benedict Tanidi; Suhadi Wido Saputro; Edy Tri Baskoro
Indonesian Journal of Combinatorics Vol 6, No 2 (2022)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2022.6.2.3

Abstract

Foster (1932) performed a mathematical census for all connected symmetric cubic (trivalent) graphs of order n with n ≤ 512. This census then was continued by Conder et al. (2006) and they obtained the complete list of all connected symmetric cubic graphs with order n ≤ 768. In this paper, we determine the total vertex irregularity strength of such graphs obtained by Foster. As a result, all the values of the total vertex irregularity strengths of the symmetric cubic graphs of order n from Foster census strengthen the conjecture stated by Nurdin, Baskoro, Gaos & Salman (2010), namely ⌈(n+3)/4⌉.

Page 7 of 8 | Total Record : 75

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