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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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Weak edge triangle free detour number of a graph Sethu Ramalingam; S. Athisayanathan
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): 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.2022.10.2.22

Abstract

For any two vertices u and v in a connected graph G = (V, E), a u − v path P is called a u − v triangle free path if no three vertices of P induce a triangle. The triangle free detour distance D△f(u, v) is the length of a longest u − v triangle free path in G. A u − v path of length D△f(u, v) is called a u − v triangle free detour. A set S ⊆ V is called a weak edge triangle free detour set of G if every edge of G has both ends in S or it lies on a triangle free detour joining a pair of vertices of S. The weak edge triangle free detour number wdn△f(G) of G is the minimum order of its weak edge triangle free detour sets and any weak edge triangle free detour set of order wdn△f(G) is a weak edge triangle free detour basis of G. Certain properties of these concepts are studied. The weak edge triangle free detour numbers of certain classes of graphs are determined. Its relationship with the triangle free detour diameter is discussed and it is proved that for any three positive integers a, b and n of integers with 3 ≤ b ≤ n − a + 1 and a ≥ 4, there exists a connected graph G of order n with triangle free detour diameter D△f = a and wdn△f(G)=b. It is also proved that for any three positive integers a, b and c with 3 ≤ a ≤ b and c ≥ b + 2, there exists a connected graph G such that R△f = a, D△f = b and wdn△f(G)=c.
The edge-distinguishing chromatic number of petal graphs, chorded cycles, and spider graphs Grant Fickes; Wing Hong Tony Wong
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): 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.2022.10.2.5

Abstract

The edge-distinguishing chromatic number (EDCN) of a graph G is the minimum positive integer k such that there exists a vertex coloring c : V(G)→{1, 2, …, k} whose induced edge labels {c(u),c(v)} are distinct for all edges uv. Previous work has determined the EDCN of paths, cycles, and spider graphs with three legs. In this paper, we determine the EDCN of petal graphs with two petals and a loop, cycles with one chord, and spider graphs with four legs. These are achieved by graph embedding into looped complete graphs.
Signless normalized Laplacian for hypergraphs Eleonora Andreotti; Raffaella Mulas
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): 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.2022.10.2.11

Abstract

The spectral theory of the normalized Laplacian for chemical hypergraphs is further investigated. The signless normalized Laplacian is introduced and it is shown that its spectrum for classical hypergraphs coincides with the spectrum of the normalized Laplacian for bipartite chemical hypergraphs. Furthermore, the spectra of special families of hypergraphs are established.
Computation of new diagonal graph Ramsey numbers Richard M. Low; Ardak Kapbasov; Arman Kapbasov; Sergey Bereg
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): 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.2022.10.2.17

Abstract

For various connected simple graphs G, we extend the table of diagonal graph Ramsey numbers R(G, G) in ‘An Atlas of Graphs.’ This is accomplished by first converting the calculation of R(G, G) into a satisfiability problem in propositional logic. Mathematical arguments and scientific computing are then used to calculate R(G, G).
On families of 2-nearly Platonic graphs Dalibor Froncek; Mahdi Reza Khorsandi; Seyed Reza Musawi; Jiangyi Qiu
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): 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.2022.10.2.23

Abstract

A 2-nearly Platonic graph of type (k|d) is a k-regular planar graph with f faces, f − 2 of which are of size d and the remaining two are of sizes d1, d2, both different from d. Such a graph is called balanced if d1 = d2. We show that all connected 2-nearly Platonic graphs are necessarily balanced. This proves a recent conjecture by Keith, Froncek, and Kreher.
On reflexive edge strength of generalized prism graphs Muhammad Irfan; Martin Baca; Andrea Semanicova-Fenovcikova
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): 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.2022.10.2.6

Abstract

Let G be a connected, simple and undirected graph. The assignments {0, 2, …, 2kv} to the vertices and {1, 2, …, ke} to the edges of graph G are called total k-labelings, where k = max{ke, 2kv}. The total k-labeling is called an reflexive edge irregular k-labeling of the graph G, if for every two different edges xy and x′y′ of G, one haswt(xy)=fv(x)+fe(xy)+fv(y)≠wt(x′y′) = fv(x′) + fe(x′y′) + fv(y′).The minimum k for which the graph G has an reflexive edge irregular k-labeling is called the reflexive edge strength of G. In this paper we investigate the exact value of reflexive edge strength for generalized prism graphs.
Motions of a connected subgraph representing a swarm of robots inside a graph of work stations Aarón Atilano; Sebastian Bejos; Christian Rubio-Montiel
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): 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.2022.10.2.12

Abstract

Imagine that a swarm of robots is given, these robots must communicate with each other, and they can do so if certain conditions are met. We say that the swarm is connected if there is at least one way to send a message between each pair of robots. A robot can move from a work station to another only if the connectivity of the swarm is preserved in order to perform some tasks. We model the problem via graph theory, we study connected subgraphs and how to motion them inside a connected graph preserving the connectivity. We determine completely the group of movements.
On regular d-handicap tournaments Bryan Freyberg; Melissa Keranen
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.2023.11.1.7

Abstract

A k-regular d-handicap tournament is an incomplete tournament in which n teams, ranked according to the natural numbers, play exactly k < n − 1 different teams exactly once and the strength of schedule of the ith ranked team is d more than the (i − 1)st ranked team for some d ≥ 1. That is, strength of schedules increase arithmetically by d with strength of team. A d-handicap distance antimagic labeling of a graph G = (V,E) of order n is a bijection ℓ : V → {1,2,…,n} with induced weight function w(xi)=Σ xj ∈ N(xi)l(xj) such that ℓ(xi)=i and the sequence of weights w(x1),w(x2),…,w(xn) forms an arithmetic sequence with difference d ≥ 1. A graph G which admits such a labeling is called a d-handicap graph.Constructing a k-regular d-handicap tournament on n teams is equivalent to finding a k-regular d-handicap graph of order n. For d = 1 and n even, the existence has recently been completely settled for all pairs (n,k), and some results are known for d = 2. For d > 2, the only known result is restricted to the case where n is divisible by 2d + 2. In this paper, we construct infinite families of d-handicap graphs where the order is not restricted to a power of 2.
The Alon-Tarsi number of two kinds of planar graphs Zhiguo Li; Qing Ye; Zeling Shao
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.2023.11.1.13

Abstract

The Alon-Tarsi number AT(G) of a graph G is the least k for which there is an orientation D of G with max outdegree k − 1 such that the number of spanning Eulerian subgraphs of G with an even number of edges differs from the number of spanning Eulerian subgraphs with an odd number of edges. In this paper, the exact value of the Alon-Tarsi number of two kinds of planar graphs is obtained.
The rainbow connection number of the enhanced power graph of a finite group Luis A. Dupont; Daniel G. Mendoza; Miriam Rodriguez
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.2023.11.1.19

Abstract

Let G be a finite group. The enhanced power graph ΓGe of G is the graph with vertex set G and two distinct vertices are adjacent if they generate a cyclic subgroup of G. In this article, we calculate the rainbow connection number of ΓGe.

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