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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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Routed planar networks David J. Aldous
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 4, No 1 (2016): 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.2016.4.1.5

Abstract

Modeling a road network as a planar graph seems very natural. However, in studying continuum limits of such networks it is useful to take {\em routes} rather than {\em edges} as primitives. This article is intended to introduce the relevant (discrete setting) notion of {\em routed network} to graph theorists. We give a naive classification of all 71 topologically different such networks on 4 leaves, and pose a variety of challenging research questions.
On total edge product cordial labeling of fullerenes Martin Baca; Muhammad Irfan; Aisha Javed; Andrea Semanicova-Fenovcikova
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 2 (2018): 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.2018.6.2.4

Abstract

For a simple graph G = (V, E) this paper deals with the existence of an edge labeling φ : E(G) → {0, 1, …, k − 1}, 2 ≤ k ≤ ∣E(G)∣, which induces a vertex labeling φ *  : V(G) → {0, 1, …, k − 1} in such a way that for each vertex v, assigns the label $\varphi(e_1)\cdot\varphi(e_2)\cdot\ldots\cdot \varphi(e_n) \pmod k$, where e1, e2, …, en are the edges incident to the vertex v. The labeling φ is called a k-total edge product cordial labeling of G if ∣(eφ(i) + vφ * (i)) − (eφ(j) + vφ * (j))∣ ≤ 1 for every i, j, $0 \le i < j \le k-1$, where eφ(i) and vφ * (i) is the number of edges and vertices with φ(e) = i and φ * (v) = i, respectively. The paper examines the existence of such labelings for toroidal fullerenes and for Klein-bottle fullerenes.
Alpha graphs with different pendent paths Christian Barrientos
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 8, No 2 (2020): 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.2020.8.2.8

Abstract

Graceful labelings are an effective tool to find cyclic decompositions of complete graphs and complete bipartite graphs. The strongest kind of graceful labeling, the α-labeling, is in the center of the research field of graph labelings, the existence of an α-labeling of a graph implies the existence of several, apparently non-related, other labelings for that graph. Furthermore, graphs with α-labelings can be combined to form new graphs that also admit this type of labeling. The standard way to combine these graphs is to identify every vertex of a base graph with a vertex of another graph. These methods have in common that all the graphs involved, except perhaps the base, have the same size. In this work, we do something different, we prove the existence of an α-labeling of a tree obtained by attaching paths of different lengths to the vertices of a base path, in such a way that the lengths of the pendent paths form an arithmetic sequence with difference one, where consecutive vertices of the base path are identified with paths which lengths are consecutive elements of the sequence. These α-trees are combined in several ways to generate new families of α-trees. We also prove that these trees can be used to create unicyclic graphs with an α-labeling. In addition, we show that the pendent paths can be substituted by equivalent α-trees to produce new α-trees, obtaining in this manner a quite robust category of α-trees.
Modular colorings of join of two special graphs N Paramaguru; R Sampathkumar
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 2, No 2 (2014): 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.2014.2.2.6

Abstract

For k≥2, a modular k-coloring of a graph G without isolated vertices is a coloring of the vertices of G with the elements in Zk having the property that for every two adjacent vertices of G, the sums of the colors of their neighbors are different in Zk. The minimum k for which G has a modular k-coloring is the modular chromatic number of G. In this paper, we determine the modular chromatic number of join of two special graphs.
Super edge-magic labeling of graphs: deficiency and maximality Anak Agung Gede Ngurah; Rinovia Simanjuntak
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 5, No 2 (2017): 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.2017.5.2.5

Abstract

A graph G of order p and size q is called super edge-magic if there exists a bijective function f from V(G) U E(G) to {1, 2, 3, ..., p+q} such that f(x) + f(xy) + f(y) is a constant for every edge $xy \in E(G)$ and f(V(G)) = {1, 2, 3, ..., p}. The super edge-magic deficiency of a graph G is either the smallest nonnegative integer n such that G U nK_1 is super edge-magic or +~ if there exists no such integer n. In this paper, we study the super edge-magic deficiency of join product graphs. We found a lower bound of the super edge-magic deficiency of join product of any connected graph with isolated vertices and a better upper bound of the super edge-magic deficiency of join product of super edge-magic graphs with isolated vertices. Also, we provide constructions of some maximal graphs, ie. super edge-magic graphs with maximal number of edges.
Bounds for graph energy in terms of vertex covering and clique numbers Hilal A. Ganie; U. Samee; S. Pirzada; Ahmad M. Alghamadi
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 7, No 2 (2019): 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.2019.7.2.9

Abstract

Let G be a simple graph with n vertices, m edges and having adjacency eigenvalues λ1, λ2, …, λn. The energy E(G) of the graph G is defined as E(G) = ∑i = 1n∣λi∣. In this paper, we obtain the upper bounds for the energy E(G) in terms of the vertex covering number τ, the clique number ω, the number of edges m, maximum vertex degree d1 and second maximum vertex degree d2 of the connected graph G. These upper bounds improve some of the recently known upper bounds.
New attack on Kotzig's conjecture Christian Barrientos; Sarah M. Minion
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 4, No 2 (2016): 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.2016.4.2.1

Abstract

In this paper we study a technique to transform $\alpha $-labeled trees into  $\rho $-labeled forests. We use this result to prove that the complete graph $K_{2n+1}$ can be decomposed into these types of forests. In addition we show a robust family of trees that admit $\rho $-labelings, we use this result to describe the set of all trees for which a $\rho $-labeling must be found to completely solve Kotzig's conjecture about decomposing cyclically the complete graph $K_{2n+1}$ into copies of any tree of size $n$.
Some bound of the edge chromatic surplus of certain cubic graphs Diamantis Koreas
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 2 (2018): 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.2018.6.2.10

Abstract

V.G. Vizing showed that any graph belongs to one of two classes: Class 1 if χʹ(G) = Δ(G) or in class 2 if χʹ(G) = Δ(G) + 1, where χʹ(G) and Δ(G) denote the edge chromatic index of G and the maximum degree of G, respectively. This paper addresses the problem of finding the edge chromatic surplus of a cubic graph G in Class 2, namely the minimum cardinality of colour classes over all 4-edge chromatic colourings of E(G). An approach to face this problem - using a new parameter q - is given in [1]. Computing q is difficult for the general case of graph G, so there is the need to find restricted classes of G, where q is easy to compute. Working in the same sense as in this paper we give an upper bound of the edge chromatic surplus for a special type of cubic graphs, that is the class of bridgeless non-planar cubic graphs in which in each pair of crossing edges, the crossing edges are adjacent to a third edge.
On a version of the spectral excess theorem Miquel Àngel Fiol; Safet Penjic
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 8, No 2 (2020): 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.2020.8.2.15

Abstract

Given a regular (connected) graph G=(X,E) with adjacency matrix A, d+1 distinct eigenvalues, and diameter D, we give a characterization  of when its distance matrix AD is a polynomial in A, in terms of the adjacency spectrum of G and the arithmetic (or harmonic) mean of the numbers of vertices at distance at most D-1 from every vertex. The same result is proved for any graph by using its Laplacian matrix L and corresponding spectrum. When D=d we reobtain the spectral excess theorem characterizing distance-regular graphs.
A new characterization of trivially perfect graphs Christian Rubio Montiel
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 3, No 1 (2015): 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.2015.3.1.3

Abstract

A graph $G$ is \emph{trivially perfect} if for every induced subgraph the cardinality of the largest set of pairwise nonadjacent vertices (the stability number) $\alpha(G)$ equals the number of (maximal) cliques $m(G)$. We characterize the trivially perfect graphs in terms of vertex-coloring and we extend some definitions to infinite graphs.

Page 5 of 39 | Total Record : 382

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