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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 325 Documents
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The strong 3-rainbow index of edge-comb product of a path and a connected graph Zata Yumni Awanis; A.N.M. Salman; Suhadi Wido Saputro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (2022): 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.2022.10.1.3

Abstract

Let G be a connected and edge-colored graph of order n, where adjacent edges may be colored the same. A tree in G is a rainbow tree if all of its edges have distinct colors. Let k be an integer with 2 ≤ k ≤ n. The minimum number of colors needed in an edge coloring of G such that there exists a rainbow tree connecting S with minimum size for every k-subset S of V(G) is called the strong k-rainbow index of G, denoted by srxk(G). In this paper, we study the srx3 of edge-comb product of a path and a connected graph, denoted by Pno⊳eH. It is clearly that |E(Pno⊳eH)| is the trivial upper bound for srx3(Pno⊳eH). Therefore, in this paper, we first characterize connected graphs H with srx3(Pno⊳eH)=|E(Pno⊳eH)|, then provide a sharp upper bound for srx3(Pno⊳eH) where srx3(Pno⊳eH)≠|E(Pno⊳eH)|. We also provide the exact value of srx3(Pno⊳eH) for some connected graphs H.
Note on decompositions based on the vertex-removing synchronised graph product Antoon Hendrik Boode
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (2022): 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.2022.10.1.9

Abstract

Recently, we have introduced two graph-decomposition theorems based on a new graph product, motivated by applications in the context of synchronising periodic real-time processes. This vertex-removing synchronised product (VRSP) is based on modifications of the well-known Cartesian product and is closely related to the synchronised product due to Wöhrle and Thomas. Here, we show how we can relax the requirements of these two graph-decomposition theorems.
Diagonal Ramsey numbers in multipartite graphs related to stars Chula Janak Jayawardene
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (2022): 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.2022.10.1.15

Abstract

Abstract: Let the star on n vertices, namely K1, n − 1 be denoted by Sn. If every two coloring of the edges of a complete balanced multipartite graph Kj × s there is a copy of Sn in the first color or a copy of Sm in the second color, then we will say Kj × s → (Sn, Sm). The size Ramsey multipartite number mj(Sn, Sm) is the smallest natural number s such that Kj × s → (Sn, Sm). In this paper, we obtain the exact values of the size Ramsey numbers mj(Sn, Sm) for n, m ≥ 3 and j ≥ 3.
On the construction of super edge-magic total graphs Darmaji Darmaji; Rinurwati Rinurwati; Suhud Wahyudi; Suhadi Wido Saputro
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 1 (2022): 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.2022.10.1.21

Abstract

Suppose G = (V, E) be a simple graph with p vertices and q edges. An edge-magic total labeling of G is a bijection f : V ∪ E → {1, 2, …, p + q} where there exists a constant r for every edge xy in G such that f(x)+f(y)+f(xy)=r. An edge-magic total labeling f is called a super edge-magic total labeling if for every vertex v ∈ V(G), f(v)≤p. The super edge-magic total graph is a graph which admits a super edge-magic total labeling. In this paper, we consider some families of super edge-magic total graph G. We construct several graphs from G by adding some vertices and edges such that the new graphs are also super edge-magic total graphs.
The locating chromatic number for m-shadow of a connected graph I Wayan Sudarsana; Faisal Susanto; Selvy Musdalifah
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): 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.2022.10.2.18

Abstract

Let c : V(G)→{1, 2, …, k} be a proper k-coloring of a simple connected graph G. Let Π = {C1, C2, …, Ck} be a partition of V(G), where Ci is the set of vertices of G receiving color i. The color code, cΠ(v), of a vertex v with respect to Π is an ordered k-tuple (d(v, C2),d(v, C2),…,d(v, Ck)), where d(v, Ci)=min{d(v, x):x ∈ Ci} for i = 1, 2, …, k. If distinct vertices have distinct color codes then c is called a locating coloring of G. The minimum k for which c is a locating coloring is the locating chromatic number of G, denoted by χL(G). Let G be a non trivial connected graph and let m ≥ 2 be an integer. The m-shadow of G, denoted by Dm(G), is a graph obtained by taking m copies of G, say G1, G2, …, Gm, and each vertex v in Gi, i = 1, 2, …, m − 1, is joined to the neighbors of its corresponding vertex v′ in Gi + 1. In the present paper, we deal with the locating chromatic number for m-shadow of connected graphs. Sharp bounds on the locating chromatic number of Dm(G) for any non trivial connected graph G and any integer m ≥ 2 are obtained. Then the values of locating chromatic number for m-shadow of complete multipartite graphs and paths are determined, some of which are considered to be optimal.
Deriving graphs with a retracting-free bidirectional double tracing Vladimir R. Rosenfeld
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): 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.2022.10.2.1

Abstract

A retracting-free bidirectional double tracing in a graph G is a closed walk which traverses every edge exactly once in each direction and such that no edge is succeeded by the same edge in the opposite direction. Studying the class Ω of all graphs admitting a retracting-free bidirectional double tracing was proposed by Ore (1951) and is, by now, of practical use to (bio)nanotechnology. In particular, this field needs various molecular polyhedra that are constructed from a single chain molecule in a retracting-free bidirectional double-tracing way.A cubic graph Q ∈ Ω has 3h edges, where h is an odd number ≥3. The graph of the triangular prism is the minimum cubic graph Q ∈ Ω, having 6 vertices and 9 edges. The graph of the square pyramid is the minimum polyhedral graph G in Ω, having 5 vertices and 8 edges.We analyze some possibilities for deriving new Ω-graphs from a given graph G ∈ Ω or G ∉ Ω using graph-theoretical operations. In particular, there was found that every noncycle Eulerian graph H admits a retracting-free bidirectional double tracing (H ∈ Ω), which is a partial solution to the problem posed by Ore.
Proximity in triangulations and quadrangulations Éva Czabarka; Peter Dankelmann; Trevor Olsen; László Székely
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): 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.2022.10.2.7

Abstract

Let G be a connected graph. If σ(v) denotes the arithmetic mean of the distances from v to all other vertices of G, then the proximity, π(G), of G is defined as the smallest value of σ(v) over all vertices v of G. We give upper bounds for the proximity of simple triangulations and quadrangulations of given order and connectivity. We also construct simple triangulations and quadrangulations of given order and connectivity that match the upper bounds asymptotically and are likely optimal.
Relaxing the injectivity constraint on arithmetic and harmonious labelings Christian Barrientos; Maged Z Youssef
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): 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.2022.10.2.13

Abstract

Several of the most studied graph labelings are injective functions, this constraint precludes some graphs from admitting such labelings; a well-known example is given by the family of trees that cannot be harmoniously labeled. In order to study the existence of these labelings for certain graphs, the injectivity constraint is often dropped. In this work we eliminate this condition for two different, but related, additive vertex labelings such as the harmonious and arithmetic labelings. The new labelings are called semi harmonious and semi arithmetic. We consider some families of graphs that do not admit the injective versions of these labelings, among the graphs considered here we have cycles and other cycle-related graphs, including the analysis of some operations like the Cartesian product and the vertex or edge amalgamation; in addition, we prove that all trees admit a semi harmonious labeling. Something similar is done with the concept of arithmetic labeling, studying finite unions of semi arithmetic graphs together with some general results.
Eternal domination and clique covering Gary MacGillivray; C. M. Mynhardt; Virgélot Virgile
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): 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.2022.10.2.19

Abstract

We study the relationship between the eternal domination number of a graph and its clique cove-ring number using both large-scale computation and analytic methods. In doing so, we answer two open questions of Klostermeyer and Mynhardt. We show that the smallest graph having its eternal domination number less than its clique covering number has 10 vertices. We determine the complete set of 10-vertex and 11-vertex graphs having eternal domination numbers less than their clique covering numbers. We show that the smallest triangle-free graph with this property has order 13, as does the smallest circulant graph. We describe a method to generate an infinite family of triangle-free graphs and an infinite family of circulant graphs with eternal domination numbers less than their clique covering numbers. We also consider planar graphs and cubic graphs. Finally, we show that for any integer k ≥ 2 there exist infinitely many graphs having domination number and eternal domination number equal to k containing dominating sets which are not eternal dominating sets.
On the outer-independent double Italian domination number Noor A'lawiah Abd Aziz; Hailiza Kamarulhaili; Farzaneh Azvin; Nader Jafari Rad
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 10, No 2 (2022): 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.2022.10.2.2

Abstract

‎An outer-independent Italian dominating function (OIIDF) on a graph G is a function f : V(G)→{0, 1, 2} such that every vertex v ∈ V(G) with f(v)=0 has at least two neighbors assigned 1 under f or one neighbor w with f(w)=2, and the set {u ∈ V(G)|f(u)=0} is independent. An outer-independent double Italian dominating function (OIDIDF) on a graph G is a function f : V(G)→{0, 1, 2, 3} such that if f(v)∈{0, 1} for a vertex v ∈ V(G), then ∑u ∈ N[v]f(u)≥3 and the set {u ∈ V(G)|f(u)=0} is independent. The weight of an OIIDF (respectively, OIDIDF) f is the value w(f)=∑v ∈ V(G)f(v). The minimum weight of an OIIDF (respectively, OIDIDF) on a graph G is called the outer-independent Italian (respectively, outer-independent double Italian) domination number of G. We characterize all trees T with outer-independent double Italian domination number twice the outer-independent Italian domination number. We also present lower bounds on the outer-independent double Italian domination number of a connected graph G in terms of the order, minimum and maximum degrees.

Page 27 of 33 | Total Record : 325

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