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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 5 Documents
 1 
Search results for , issue "Vol 7, No 2 (2023)" : 5 Documents clear
Exploring the Power of Graph Theory in Hadron Theory: From Bound States to Quark Systems Abu-shady, M.
Indonesian Journal of Combinatorics Vol 7, No 2 (2023)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2023.7.2.5

Abstract

The article discusses how graph theory has been utilized in hadron theory for high energy interactions in recent years. The paper emphasizes the significance of a visual perspective throughout the discussion and explores how graph theory can aid in creating various systems such as bound state systems. Additionally, the paper delves into how graph theory has been used to develop few-body quark systems and how it can connect with adjacency and incidence matrices in the graph theory by providing examples of how these fundamental principles have been applied to topics ranging from hadronic bound states.
On the metric dimension of Buckminsterfullerene-net graph Yulianti, Lyra; Welyyanti, Des; Yanita, Yanita; Fajri, Muhammad Rafif; Saputro, Suhadi Wido
Indonesian Journal of Combinatorics Vol 7, No 2 (2023)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2023.7.2.2

Abstract

The metric dimension of an arbitrary connected graph G, denoted by dim(G), is the minimum cardinality of the resolving set W of G. An ordered set W = {w1, w2,..., wk} is a resolving set of G if for all two different vertices in G, their metric representations are different with respect to W. The metric representation of a vertex v with respect to W is defined as k-tuple r(v|W) = (d(v,w1), d(v,w2),..., d(v,wk)), where d(v,wj) is the distance between v and wj for 1 ≤ j ≤ k. The Buckminsterfullerene graph is a 3-reguler graph on 60 vertices containing some cycles C5 and C6. Let B60t denotes the tth  B60 for 1 ≤ t ≤ m and m ≥ 2. Let vt be a terminal vertex for each B60t. The Buckminsterfullerene-net, denoted by H:=Amal{B60t,v| 1 ≤ t ≤ m; m ≥ 2} is a graph constructed from the identification of all terminal vertices vt, for 1 ≤ t ≤ m and m ≥ 2, into a new vertex, denoted by v. This paper will determine the metric dimension of the Buckminsterfullerene-net graph H.
A note on Second Degrees in Graphs Naji, Ahmed Mohammed
Indonesian Journal of Combinatorics Vol 7, No 2 (2023)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2023.7.2.3

Abstract

The second degree of a node x in a graph Γ=(V,E), denoted by deg2(x), is the number of nodes at distance two from x in a graph Γ. In the present article, we are interested in examination of the second degrees properties in a graph. The old bounds and the general formulas of the second degree of some graph operations are collected. We provide an improvement on the useful result "deg2(x) ≤  (∑(y ∈ N(x)) deg(y)) - deg(x), for every x ∈ V(Γ)", by adding a term of the triangles number in a graph, in order to the equality holds for each quadrangle-free graph. Further, upper and lower bounds for the maximum and minimum second degrees are established. Finally the second degree-sum formula are derived. In addition, bounds on second degree-sum are also established.
4-Dimensional Lattice Path Enumeration with Arbitrary Steps Vural, Alper; Karaçam, Cemil
Indonesian Journal of Combinatorics Vol 7, No 2 (2023)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2023.7.2.1

Abstract

Consider a set of vectors, L, which consists of vectors whose coordinates are 0 or 1. We find explicit formulas that counts the number of lattice paths from origin to (a,b,c,d) for using vectors in {(1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,0,1)} ∪ L for various choices of L. In some cases we also give the recursive formulas for the same problem. Next we determine the minimum number of vectors that must be used to reach (a,b,c,d), also called the minimum distance problem, for different sets of vectors.
On inclusive distance vertex irregularity strength of book graph Wahyu, Ria Ammelia; Santoso, Kiswara Agung; Slamin, Slamin
Indonesian Journal of Combinatorics Vol 7, No 2 (2023)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2023.7.2.4

Abstract

The concept of distance vertex irregular labeling of graphs was introduced by Slamin in 2017. The distance vertex irregular labeling on a graph G with v vertices is defined as an assignment λ : V → {1, 2, ..., k} so that the weights calculated at vertices are distinct. The weight of a vertex x in G is defined as the sum of the labels of all the vertices adjacent to x (distance 1 from x). The distance vertex irregularity strength of graph G, denoted by dis(G), is defined as the minimum value of the largest label k over all such irregular assignments. Bong, Lin and Slamin generalized the concept to inclusive and non-inclusive distance irregular labeling. The difference between them depends on the way to calculate the weight on the vertex whether the vertex label we calculate its weight is included or not. The inclusive distance vertex irregularity strength of G, is defined as the minimum of the largest label k over all such inclusive irregular assignments. In this paper, we determine the inclusive distance vertex irregularity strength of some particular classes of graphs such as book graph.

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