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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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Outer independent global dominating set of trees and unicyclic graphs Doost Ali Mojdeh; Mortaza Alishahi
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.2019.7.1.10

Abstract

Let G be a graph. A set D ⊆ V(G) is a global dominating set of G if D is a dominating set of G and $\overline G$. γg(G) denotes global domination number of G. A set D ⊆ V(G) is an outer independent global dominating set (OIGDS) of G if D is a global dominating set of G and V(G) − D is an independent set of G. The cardinality of the smallest OIGDS of G, denoted by γgoi(G), is called the outer independent global domination number of G. An outer independent global dominating set of cardinality γgoi(G) is called a γgoi-set of G. In this paper we characterize trees T for which γgoi(T) = γ(T) and trees T for which γgoi(T) = γg(T) and trees T for which γgoi(T) = γoi(T) and the unicyclic graphs G for which γgoi(G) = γ(G), and the unicyclic graphs G for which γgoi(G) = γg(G).
Odd sum labeling of graphs obtained by duplicating any edge of some graphs S. Arockiaraj; P. Mahalakshmi; P. Namasivayam
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 3, No 2 (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.2015.3.2.8

Abstract

An injective function $f:V(G)\rightarrow \{0,1,2,\dots,q\}$ is an odd sum labeling if the induced edge labeling $f^*$ defined by $f^*(uv)=f(u)+f(v),$ for all $uv\in E(G),$ is bijective and $f^*(E(G))=\{1,3,5,\dots,2q-1\}.$ A graph is said to be an odd sum graph if it admits an odd sum labeling. In this paper we study the odd sum property of graphs obtained by duplicating any edge of some graphs.
List graphs and distance-consistent node labelings Håkan Lennerstad; Mattias Eriksson
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 1 (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.2018.6.1.11

Abstract

In this paper we consider node labelings c of an undirected connected graph G = (V, E) with labels {1, 2, ..., ∣V∣}, which induce a list distance c(u, v) = ∣c(v) − c(u)∣ besides the usual graph distance d(u, v). Our main aim is to find a labeling c so c(u, v) is as close to d(u, v) as possible. For any graph we specify algorithms to find a distance-consistent labeling, which is a labeling c that minimize $\sum\limits_{u,v\in V} (c(u,v)-d(u,v)) ^2$. Such labeliings may provide structure for very large graphs. Furthermore, we define a labeling c fulfilling d(u1, v1) < d(u2, v2) ⇒ c(u1, v1) ≤ c(u2, v2) for all node pairs u1, v1 and u2, v2 as a list labeling, and a graph that has a list labeling is a list graph. We prove that list graphs exist for all n = ∣V∣ and all k = ∣E∣ : n − 1 ≤ k ≤ n(n − 1)/2, and establish basic properties. List graphs are hamiltonian, and show weak versions of properties of path graphs.
Two classes of non-Leech trees Seena Varghese; Aparna Lakshmanan S; Subramanian Arumugam
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.2020.8.1.15

Abstract

Let T be a tree of order n. For any edge labeling f : E → {1,2,3,...} the weight of a path P is the sum of the labels of the edges of P and is denoted by w(P). If the weights of the nC2 paths in T are exactly 1, 2,...,nC2, then f is called a Leech labeling and a tree which admits a Leech labeling is called a Leech tree. In this paper we determine all Leech trees having diameter three. We also prove that the tree obtained from the path Pn =(v1,v2,...,vn) by attaching a pendent vertex at vn-1 is not a Leech tree for all n ≥ 4.
New measures of graph irregularity Clive Elphick; Pawel Wocjan
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.2014.2.1.5

Abstract

In this paper, we define and compare three new measures of graph irregularity. We use these measures to tighten upper bounds for the chromatic number and the Colin de Verdiere parameter. We also strengthen the concise Turan theorem for irregular graphs and investigate to what extent Turan's theorem can be similarly strengthened for generalized r-partite graphs. We conclude by relating these new measures to the Randic index and using the measures to devise new normalised indices of network heterogeneity. 
On an edge partition and root graphs of some classes of line graphs K Pravas; A. Vijayakumar
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.2017.5.1.12

Abstract

The Gallai and the anti-Gallai graphs of a graph $G$ are complementary pairs of spanning subgraphs of the line graph of $G$. In this paper we find some structural relations between these graph classes by finding a partition of the edge set of the line graph of a graph $G$ into the edge sets of the Gallai and anti-Gallai graphs of $G$. Based on this, an optimal algorithm to find the root graph of a line graph is obtained. Moreover, root graphs of diameter-maximal, distance-hereditary, Ptolemaic and chordal graphs are also discussed.
Block circulant graphs and the graphs of critical pairs of crowns Rebecca E. Garcia; Pamela E. Harris; Bethany Kubik; Shannon Talbott
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.2019.7.2.1

Abstract

In this paper, we provide a natural bijection between a special family of block circulant graphs and the graphs of critical pairs of the posets known as generalized crowns. In particular, every graph in this family of block circulant graphs we investigate has a generating block row that follows a symmetric growth pattern of the all ones matrix. The natural bijection provides an upper bound on the chromatic number for this infinite family of graphs.
Constructing arbitrarily large graphs with a specified number of Hamiltonian cycles Michael Haythorpe
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.2016.4.1.3

Abstract

A constructive method is provided that outputs a directed graph which is named a broken crown graph, containing $5n-9$ vertices and $k$ Hamiltonian cycles for any choice of integers $n \geq k \geq 4$. The construction is not designed to be minimal in any sense, but rather to ensure that the graphs produced remain non-trivial instances of the Hamiltonian cycle problem even when $k$ is chosen to be much smaller than $n$.
The structure of graphs with forbidden induced $C_4$, $\overline{C}_4$, $C_5$, $S_3$, chair and co-chair Salman Ghazal
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.2018.6.2.2

Abstract

We find the structure of graphs that have no C4, $\overline{C}_4$, C5, S3, chair and co-chair as induced subgraphs. Then we deduce the structure of the graphs having no induced C4, $\overline{C_4}$, S3, chair and co-chair and the structure of the graphs G having no induced C4, $\overline{C_4}$ and such that every induced P4 of G is contained in an induced C5 of G.
Resistors in dual networks Martina Furrer; Norbert Hungerbühler; Simon Jantschgi
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.2020.8.2.6

Abstract

Let G be a finite plane multigraph and G' its dual. Each edge e of G is interpreted as a resistor of resistance Re, and the dual edge e' is assigned the dual resistance Re':=1/Re. Then the equivalent resistance re over e and the equivalent resistance re' over e' satisfy re/Re+re'/Re'=1. We provide a graph theoretic proof of this relation by expressing the resistances in terms of sums of weights of spanning trees in G and G' respectively.

Page 17 of 39 | Total Record : 382

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