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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 9 Documents
 1 
Search results for , issue "Vol 2, No 2 (2014): Electronic Journal of Graph Theory and Applications" : 9 Documents clear
Fibonacci number of the tadpole graph Joe DeMaio; John Jacobson
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.2014.2.2.5

Abstract

In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2) and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph via algebraic and combinatorial methods.
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.
On open neighborhood locating-dominating in graphs Mustapha Chellali; Nader Jafari Rad; Suk Jai Seo; Peter James Slater
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.2014.2.2.1

Abstract

A set D of vertices in a graph G = (V (G), E(G)) is an open neighborhood locating-dominating set (OLD-set) for G if for every two vertices u, v of V (G) the sets N(u) ∩ D and N(v) ∩ D are non-empty and different. The open neighborhood locating-dominating number OLD(G) is the minimum cardinality of an OLD-set for G. In this paper we characterize graphs G of order n with OLD(G) = 2, 3, or n and graphs with minimum degree (G) ≥ 2 that are C4-free with OLD(G) = n-1.
On k-geodetic digraphs with excess one Anita Abildgaard Sillasen
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.2014.2.2.7

Abstract

A k-geodetic digraph G is a digraph in which, for every pair of vertices u and v (not necessarily distinct), there is at most one walk of length at most k from u to v. If the diameter of G is k, we say that G is strongly geodetic. Let N(d,k) be the smallest possible order for a k-geodetic digraph of minimum out-degree d, then N(d,k) is at most 1+d+d^2+...+d^k=M(d,k), where M(d,k) is the Moore bound obtained if and only if G is strongly geodetic. Thus strongly geodetic digraphs only exist for d=1 or k=1, hence for d,k >1 we wish to determine if N(d,k)=M(d,k)+1 is possible. A k-geodetic digraph with minimum out-degree d and order M(d,k)+1 is denoted as a (d,k,1)-digraph or said to have excess 1.In this paper we will prove that a (d,k,1)-digraph is always out-regular and that if it is not in-regular, then it must have 2 vertices of in-degree less than d, d vertices of in-degree d+1 and the remaining vertices will have in-degree d.Furthermore we will prove there exist no (2,2,1)-digraphs and no diregular (2,k,1)-digraphs for k> 2.
Fault-tolerant designs in lattice networks on the Klein bottle Ayesha Shabbir
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.2014.2.2.2

Abstract

In this note, we consider triangular, square and hexagonal lattices on the flat Klein bottle, and find subgraphs with the property that for any $j$ vertices there exists a longest path (cycle) avoiding all of them. This completes work previously done in other lattices.
A note on edge-disjoint contractible Hamiltonian cycles in polyhedral maps Ashish K Upadhyay; Dipendu Maity
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.2014.2.2.8

Abstract

We present a necessary and sufficient condition for existence of edge-disjoint contractible Hamiltonian Cycles in the edge graph of polyhedral maps.
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.
Algebraic and computer-based methods in the undirected degree/diameter problem - A brief survey Hebert Perez-Roses
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.2014.2.2.9

Abstract

This paper discusses the most popular algebraic techniques and computational methods that have been used to construct large graphs with given degree and diameter.
A remark on star-C4 and wheel-C4 Ramsey numbers Yanbo Zhang; Hajo Broersma; Yaojun Chen
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.2014.2.2.3

Abstract

Given two graphs G1 and G2, the Ramsey number R(G1;G2)is the smallest integer N such that, for any graph G of order N, either G1 is a subgraph of G, or G2 is a subgraph of the complement of G. Let Cn denote a cycle of order n, Wn a wheel of order n+1 and Sn a star of order n. In this paper, it is shown that R(Wn;C4) = R(Sn+1;C4) for n ≥ 6. Based on this result and Parsons' results on R(Sn+1;C4), we establish the best possible general upper bound for R(Wn;C4) and determine some exact values for R(Wn;C4).

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