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INDONESIA
Electronic Journal of Graph Theory and Applications (EJGTA)
Published by Indonesian Combinatorial Society
ISSN : 23382287     EISSN : -     DOI : -
Core Subject : Engineering,
Electrical & Electronics Engineering
The Electronic Journal of Graph Theory and Applications (EJGTA) is a refereed journal devoted to all areas of modern graph theory together with applications to other fields of mathematics, computer science and other sciences. The journal is published by the Indonesian Combinatorial Society (InaCombS), Graph Theory and Applications (GTA) Research Group - The University of Newcastle - Australia, and Faculty of Mathematics and Natural Sciences - Institut Teknologi Bandung (ITB) Indonesia. Subscription to EJGTA is free. Full-text access to all papers is available for free. All research articles as well as surveys and articles of more general interest are welcome. All papers will be refereed in the normal manner of mathematical journals to maintain the highest standards. This journal is sponsored by CARMA (Computer-Assisted Research Mathematics and its Applications) Priority Research Centre - The University of Newcastle - Australia, and Study Program of Information System- University of Jember - Indonesia.
Arjuna Subject : -
Articles 382 Documents
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Zonal graphs of small cycle rank Andrew Bowling; Ping Zhang
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 1 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2023.11.1.1

Abstract

A zonal labeling of a plane graph G is an assignment of the two nonzero elements of the ring Z3 of integers modulo 3 to the vertices of G such that the sum of the labels of the vertices on the boundary of each region of G is the zero element of Z3. A plane graph possessing such a labeling is a zonal graph. There is a connection between zonal labelings of connected bridgeless cubic plane graphs and the Four Color Theorem. Zonal labelings of cycles play a role in this connection. The cycle rank of a connected graph of order n and size m is m − n + 1. Thus, cycles have cycle rank 1. All zonal connected graphs of cycle rank at most 2 are determined.
An algebraic approach to sets defining minimal dominating sets of regular graphs Mehrdad Nasernejad
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 2 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2023.11.2.5

Abstract

Suppose that V = {1, …, n} is a non-empty set of n elements, S = {S1, …, Sm} a non-empty set of m non-empty subsets of V. In this paper, by using some algebraic notions in commutative algebra, we investigate the question arises whether there exists an undirected finite simple graph G with V(G)=V, where S is the set whose elements are the minimal dominating sets of G.
Linear codes and cyclic codes over finite rings and their generalizations: a survey Djoko Suprijanto
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 2 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2023.11.2.11

Abstract

We survey a recent progress of cyclic codes over finite rings and their generalization to skew cyclic as well as skew cyclic codes with derivation over finite rings, focusing on structural properties of the codes. We also report recent developments on the construction methods of linear codes from graphs, in particular strongly regular as well as distance regular graphs.
(1, 2)-rainbow connection number at most 3 in connected dense graphs Trung Duy Doan; Le Thi Duyen
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 2 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2023.11.2.6

Abstract

Let G be an edge-coloured connected graph G. A path P in the graph G is called l-rainbow path if each subpath of length at most l + 1 is rainbow. The graph G is called (k, l)-rainbow connected if any two vertices in G are connected by at least k pairwise internally vertex-disjoint l-rainbow paths. The smallest number of colours needed in order to make G (k, l)-rainbow connected is called the (k, l)-rainbow connection number of G and denoted by rck, l(G). In this paper, we consider the (1, 2)-rainbow connection number at most 3 in some connected dense graphs. Our main results are as follows: (1) Let n ≥ 7 be an integer and G be a connected graph of order n. If ω(G)≥n − 3, then rc1, 2(G)≤3. Moreover, the bound of the clique number is sharpness. (2) Let n ≥ 7 be an integer and G be a connected graph of order n. If |E(G)| ≥ C(n − 3, 2)+7, then rc1, 2(G)≤3.
On the problems of CF-connected graphs Michal Staš; Juraj Valiska
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 2 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2023.11.2.12

Abstract

The crossing number cr(G) of a graph G is the minimum number of edge crossings over all drawings of G in the plane, and the optimal drawing of G is any drawing at which the desired minimum number of crossings is achieved. We conjecture that a complete graph Kn is CF-connected if and only if it does not contain a subgraph of K8, where a connected graph G is CF-connected if there is a path between every pair of vertices with no crossing on its edges for each optimal drawing of G. We establish the validity of this Conjecture for the complete graphs Kn for any n ≤ 12, and by assuming the Harary-Hill’s Conjecture that cr(Kn)=H(n)=1/4⌊n/2⌋⌊n − 1/2⌋⌊n − 2/2⌋⌊n − 3/2⌋ is also valid for all n > 12. The proofs of this paper are based on the idea of a new concept of a crossing sequence.
Graceful labeling construction for some special tree graph using adjacency matrix Nikson Simarmata; Ikhlas Pratama Sandy; Kiki A. Sugeng
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 2 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2023.11.2.1

Abstract

In 1967, Rosa introduced β − labeling which was then popularized by Golomb under the name graceful. Graceful labeling on a graph G is an injective function f : V(G)→{0, 1, 2, …, |E(G)|} such that, when each edge uv ∈ E(G) is assigned the label |f(u)−f(v)| the resulting edge labels are distinct. If graph G has graceful labeling then G is called a graceful graph. Rosa also introduced α − labeling on graph G which is a graceful labeling f with an additional condition that there is λ ∈ {1, 2, …, |E(G)|} so that for every edge uv ∈ E(G) where f(u)<f(v) then f(u)≤λ < f(v). This paper gives a new approach to showing a graph is admitted α − labeling using an adjacency matrix. Then this construction will be used to construct graceful labeling for the superstar graph. Moreover, we give a graceful labeling construction for a super-rooted tree graph.
Signed graphs and signed cycles of hyperoctahedral groups Ryo Uchiumi
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 2 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2023.11.2.7

Abstract

For a graph with edge ordering, a linear order on the edge set, we obtain a permutation of vertices by considering the edges as transpositions of endvertices. It is known from Dénes’ results that the permutation of a tree is a full cyclic for any edge ordering. As a corollary, Dénes counted up the number of representations of a full cyclic permutation by means of product of the minimal number of transpositions. Moreover, a graph with an edge ordering which the permutation is a full cyclic is characterized by graph embedding. In this article, we consider an analogy of these results for signed graphs and hyperoctahedral groups. We give a necessary and sufficient condition for a signed graph to have an edge ordering such that the permutation is an even (or odd) full cyclic. We show that the edge ordering of the signed tree with some loops always gives an even (or odd) full cyclic permutation and count up the number of representations of an odd full cyclic permutation by means of product of the minimal number of transpositions.
On matching number, decomposition and representation of well-formed graph Alex Ralph Baisa Nieva; Karen P. Nocum
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 2 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2023.11.2.13

Abstract

In this paper, we find a special type of non-traceable cubic bridge graph called well-formed graph whose central fragment is isomorphic to a hairy cycle and whose branches are pairwise isomorphic. We then show that a well-formed graph can be partition into isomorphic subgraph. Some properties of a well-formed graph such as perfect matching, matching number, decomposition and some parameters for pictorial representation are also provided.
Multiplicity-free gonality on graphs Frances Dean; Max Everett; Ralph Morrison
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 2 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2023.11.2.2

Abstract

The divisorial gonality of a graph is the minimum degree of a positive rank divisor on that graph. We introduce the multiplicity-free gonality of a graph, which restricts our consideration to divisors that place at most 1 chip on each vertex. We give a sufficient condition in terms of vertex-connectivity for these two versions of gonality to be equal; and we show that no function of gonality can bound multiplicity-free gonality, even for simple graphs. We also prove that multiplicity-free gonality is NP-hard to compute, while still determining it for graph families for which gonality is currently unknown. We also present new gonalities, such as for the wheel graphs.
Variations on Ramsey numbers and minimum numbers of monochromatic triangles in line $2$-colorings of configurations Jamie Bishop; Rebekah Kuss; Benjamin Peet
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 2 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2023.11.2.8

Abstract

This paper begins by exploring some old and new results about Ramsey numbers and minimum numbers of monochromatic triangles in 2-colorings of complete graphs, both in the disjoint and non-disjoint cases. We then extend the theory, by defining line 2-colorings of configurations of points and lines and considering the minimum number of non-disjoint monochromatic triangles. We compute specific examples for notable symmetric v3 configurations before considering a general result regarding the addition or connected sum of configurations through incidence switches. The paper finishes by considering the maximal number of mutually intersecting lines and how this relates to the minimum number of triangles given a line 2-coloring of a symmetric v3 configuration.

Page 32 of 39 | Total Record : 382

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