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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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Three-colour bipartite Ramsey number R_b(G_1,G_2,P_3) R Lakshmi; D.G. Sindhu
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 8, No 1 (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.2020.8.1.14

Abstract

For simple bipartite graphs G1, G2, G3, the three-colour bipartite graph Ramsey number Rb(G1,G2,G3) is defined as the least positive integer n such that any 3-edge-colouring of Kn,n assures a monochromatic copy of Gi in the ith colour for some i, i ∈ {1,2,3}. In this paper, we consider the three-colour bipartite Ramsey number Rb(G1,G2,P3). Exact values are determined when G1 = G2 = C4 and when (G1,G2) = (a bistar, a bistar). For integers m,n ≥ 2, a recursive upper bound, Rb(Km,m,Kn,n,P3) ≤ Rb(Km-1,m-1,Kn,n,P3) + Rb(Km,m,Kn-1,n-1,P3) + 3,  is given. When G1 and G2 are even cycles, a lower bound is provided. In addition to these results, we have obtained the relations: R(G,K1,n) ≤ Rb(G,K1,n+1) and R(G,H) ≤ Rb(G,H,P3).
Antimagicness for a family of generalized antiprism graphs Dominique Buset; Mirka Miller; Oudone Phanalasy; Joe Ryan
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 2, No 1 (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.2014.2.1.4

Abstract

An antimagic labeling of a graph $G=(V,E)$ is a bijection from the set of edges $E$ to the set of integers $\{1,2,\dots, |E|\}$ such that all vertex weights are pairwise distinct, where the weight of a vertex is the sum of all edge labels incident with that vertex. A graph is antimagic if it has an antimagic labeling. In this  paper we provide constructions of antimagic labelings for a family of generalized antiprism graphs and generalized toroidal antiprism graphs.
Spectra of graphs and the spectral criterion for property (T) Alain Valette
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 5, No 1 (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.2017.5.1.11

Abstract

For a finite connected graph $X$, we consider the graph $RX$ obtained from $X$ by associating a new vertex to every edge of $X$ and joining by edges the extremities of each edge of $X$ to the corresponding new vertex. We express the spectrum of the Laplace operator on $RX$ as a function of the corresponding spectrum on $X$. As a corollary, we show that $X$ is a complete graph if and only if $\lambda_1(RX)>\frac{1}{2}$. We give a re-interpretation of the correspondence $X\mapsto RX$ in terms of the right-angled Coxeter group defined by $X$.
The cycle (circuit) polynomial of a graph with double and triple weights of edges and cycles Vladimir R. Rosenfeld
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 7, No 1 (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.2019.7.1.15

Abstract

Farrell introduced the general class of graph polynomials which he called the family polynomials, or F-polynomials, of graphs. One of these is the cycle, or circuit, polynomial. This polynomial is in turn a common generalization of the characteristic, permanental, and matching polynomials of a graph, as well as a wide variety of statistical-mechanical partition functions, such as were earlier known.  Herein, we specially derive weighted generalizations of the characteristic and permanental polynomials requiring for calculation thereof to assign double (res. triple) weights to all Sachs subgraphs of a graph. To elaborate an analytical method of calculation, we extend our earlier differential-operator approach which is now employing operator matrices derived from the adjacency matrix. Some theorematic results are obtained.
Weighted graphs: Eigenvalues and chromatic number Charles Delorme
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.2016.4.1.2

Abstract

We revisit Hoffman relation involving chromatic number $\chi$ and eigenvalues. We construct some graphs and weighted graphs such that the largest and smallest eigenvalues $\lambda$ dan $\mu$ satisfy $\lambda=(1-\chi)\mu.$ We study in particular the eigenvalues of the integer simplex $T_m^2,$ a 3-chromatic graph on $\binom {m+2}{2}$ vertices.
On regular handicap graphs of order $n \equiv 0$ mod 8 Dalibor Froncek; Aaron Shepanik
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.2018.6.2.1

Abstract

A handicap distance antimagic labeling of a graph G = (V, E) with n vertices is a bijection f̂ : V → {1, 2, …, n} with the property that f̂(xi) = i, the weight w(xi) is the sum of labels of all neighbors of xi, and the sequence of the weights w(x1), w(x2), …, w(xn) forms an increasing arithmetic progression. A graph G is a handicap distance antimagic graph if it allows a handicap distance antimagic labeling. We construct r-regular handicap distance antimagic graphs of order $n \equiv 0 \pmod{8}$ for all feasible values of r.
Totally irregular total labeling of some caterpillar graphs Diari Indriati; W. Widodo; Indah E. Wijayanti; Kiki A. Sugeng; Isnaini Rosyida
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.2020.8.2.5

Abstract

Assume that G(V,E) is a graph with V and E as its vertex and edge sets, respectively. We have G is simple, connected, and undirected. Given a function λ from a union of V and E into a set of k-integers from 1 until k. We call the function λ as a totally irregular total k-labeling if the set of weights of vertices and edges consists of different numbers. For any u ∈ V, we have a weight wt(u)=λ(u)+ ∑{uy ∈ E} λ(uy). Also, it is defined a weight wt(e)= λ(u)+ λ(uv) + λ(v) for each e=uv ∈ E. A minimum k used in k-total labeling λ is named as a total irregularity strength of G, symbolized by ts(G). We discuss results on ts of some caterpillar graphs in this paper. The results are ts(S{p,2,2,q}) = ⌈ (p+q-1)/2 ⌉ for p, q greater than or equal to 3, while ts(S{p,2,2,2,p}) = ⌈(2p-1)/2 ⌉, p ≥ 4.
H-E-Super magic decomposition of graphs S.P. Subbiah; J. Pandimadevi
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.2014.2.2.4

Abstract

An H-magic labeling in an H-decomposable graph G is a bijection f:V(G) U E(G) --> {1,2, … ,p+q} such that for every copy H in the decomposition, $\sum\limits_{v\in V(H)} f(v)+\sum\limits_{e\in E(H)} f(e)$ is constant. The function f is said to be H-E-super magic if f(E(G)) = {1,2, … ,q}. In this paper, we study some basic properties of m-factor-E-super magic labelingand we provide a necessary and sufficient condition for an even regular graph to be 2-factor-E-super magic decomposable. For this purpose, we use Petersen's theorem and magic squares.
Open-independent, open-locating-dominating sets Suk J. Seo; Peter J. Slater
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.2017.5.2.2

Abstract

A distinguishing set for a graph G = (V, E) is a dominating set D, each vertex $v \in D$ being the location of some form of a locating device, from which one can detect and precisely identify any given "intruder" vertex in V(G).  As with many applications of dominating sets, the set $D$ might be required to have a certain property for <D>, the subgraph induced by D (such as independence,  paired, or connected).  Recently  the study of independent locating-dominating sets and independent identifying codes was initiated.  Here we introduce the property of open-independence for open-locating-dominating sets.
The second least eigenvalue of the signless Laplacian of the complements of trees Muhammad Ajmal; Masood Ur Rehman; Tayyab Kamran
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.2019.7.2.6

Abstract

Suppose that Tnc is a set, such that the elements of Tnc are the complements of trees of order n. In 2012, Li and Wang gave the unique graph in the set Tnc ∖ {K1, n − 1c} with minimum 1st ‘least eigenvalue of the signless Laplacian’ (abbreviated to a LESL). In the present work, we give the unique graph with 2nd LESL in Tnc ∖ {K1, n − 1c}, where K1, n − 1c represents the complement of star of order n.

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