##### Location , INDONESIA
Electronic Journal of Graph Theory and Applications (EJGTA)
ISSN : 23382287     EISSN : -     DOI : -
Core Subject : 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 194 Documents
Block circulant graphs and the graphs of critical pairs of crowns Garcia, Rebecca E.; Harris, Pamela E.; Kubik, Bethany; Talbott, Shannon
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

#### 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.
New measures of graph irregularity Elphick, Clive; Wocjan, Pawel
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

#### 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 VerdiereÂ 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.Â
On an edge partition and root graphs of some classes of line graphs Pravas, K; Vijayakumar, A.
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

#### 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.
Two classes of non-Leech trees Varghese, Seena; S, Aparna Lakshmanan; Arumugam, Subramanian
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

#### Abstract

Let T be a tree of order n. For any edge labeling f : E â†’ {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 nC2Â 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 PnÂ =(v1,v2,...,vn) by attaching a pendent vertex at vn-1Â is not a Leech tree for all n â‰¥ 4.
List graphs and distance-consistent node labelings Lennerstad, HÃ¥kan; Eriksson, Mattias
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

#### Abstract

In this paper we consider node labelings c of an undirected connected graph Gâ€„=â€„(V,â€†E) with labels {1,â€†2,â€†...,â€†âˆ£Vâˆ£}, which induce a list distance c(u,â€†v)â€„=â€„âˆ£c(v)â€…âˆ’â€…c(u)âˆ£ besides the usual graph distance d(u,â€†v). Our main aim is to find a labeling c so c(u,â€†v) is as close to d(u,â€†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,â€†v1)â€„<â€„d(u2,â€†v2)â€„â‡’â€„c(u1,â€†v1)â€„â‰¤â€„c(u2,â€†v2) for all node pairs u1,â€†v1 and u2,â€†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 nâ€„=â€„âˆ£Vâˆ£ and all kâ€„=â€„âˆ£Eâˆ£â€„:â€„nâ€…âˆ’â€…1â€„â‰¤â€„kâ€„â‰¤â€„n(nâ€…âˆ’â€…1)/2, and establish basic properties. List graphs are hamiltonian, and show weak versions of properties of path graphs.
Outer independent global dominating set of trees and unicyclic graphs Mojdeh, Doost Ali; Alishahi, Mortaza
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

#### Abstract

Let G be a graph. A set Dâ€„âŠ†â€„V(G) is a global dominating set of G if D is a dominating set of G and $\overline G$. Î³g(G) denotes global domination number of G. A set Dâ€„âŠ†â€„V(G) is an outer independent global dominating set (OIGDS) of G if D is a global dominating set of G and V(G)â€…âˆ’â€…D is an independent set of G. The cardinality of the smallest OIGDS of G, denoted by Î³goi(G), is called the outer independent global domination number of G. An outer independent global dominating set of cardinality Î³goi(G) is called a Î³goi-set of G. In this paper we characterize trees T for which Î³goi(T)â€„=â€„Î³(T) and trees T for which Î³goi(T)â€„=â€„Î³g(T) and trees T for which Î³goi(T)â€„=â€„Î³oi(T) and the unicyclic graphs G for which Î³goi(G)â€„=â€„Î³(G), and the unicyclic graphs G for which Î³goi(G)â€„=â€„Î³g(G).
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

#### Abstract

Let $G = (V,E)$ be a simple connected graph. Theeccentric-distance sum of $G$ is defined as$\xi^{ds}(G) =\ds\sum_{\{u,v\}\subseteq V(G)} [e(u)+e(v)] d(u,v)$, where $e(u)$ %\dsis the eccentricity of the vertex $u$ in $G$ and $d(u,v)$ is thedistance between $u$ and $v$. In this paper, we establish formulaeto calculate the eccentric-distance sum for some graphs, namelywheel, star, broom, lollipop, double star, friendship, multi-stargraph and the join of $P_{n-2}$ and $P_2$.
On irregularity strength of disjoint union of friendship graphs Ahmad, Ali; Baca, Martin; Numan, Muhammad
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 1, No 2 (2013): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

#### Abstract

We investigate the vertex total and edge total modication of the well-known irregularity strength of graphs. We have determined the exact values of the total vertex irregularity strength and the total edge irregularity strength of a disjoint union of friendship graphs.
Congruences and subdirect representations of graphs Veldsman, Stefan
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

#### Abstract

A basic tool in universal algebra is that of a congruence. It has been shown that congruences can be definedÂ  for graphs with properties similar to their universal algebraic counterparts. In particular, a subdirect product of graphs and hence also a subdirectly irreducible graph, can be expressed in terms of graph congruences. Here the subdirectly irreducible graphs are determined explicitly. Using congruences, a graph theoretic version of the well-known Birkhoff Theorem from universal algebra is given. This shows that any non-trivial graph is a subdirect product of subdirectly irreducible graphs
On inclusive distance vertex irregular labelings Baca, Martin; Semanicova-Fenovcikova, Andrea; Slamin, S.; Sugeng, Kiki A.
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

#### Abstract

For a simple graph G, a vertex labeling fâ€„:â€„V(G)â€„â†’â€„{1,â€†2,â€†...,â€†k} is called a k-labeling. The weight of a vertex v, denoted by wtf(v) is the sum of all vertex labels of vertices in the closed neighborhood of the vertex v. A vertex k-labeling is defined to be an inclusive distance vertex irregular distance k-labeling of G if for every two different vertices u and v there is wtf(u)â€„â‰ â€„wtf(v). The minimum k for which the graph G has a vertex irregular distance k-labeling is called the inclusive distance vertex irregularity strength of G. In this paper we establish a lower bound of the inclusive distance vertex irregularity strength for any graph and determine the exact value of this parameter for several families of graphs.

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