Articles
On regular handicap graphs of order $n equiv 0$ mod 8
Froncek, Dalibor ( Department of Mathematics and Statistics, University of Minnesota Duluth
Duluth, USA ) , Shepanik, Aaron ( Department of Mathematics and Statistics, University of Minnesota Duluth
Duluth, USA )
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
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A handicap distance antimagic labeling of a graph G = (V, E) with n vertices is a bijection fÌ : V â {1, 2, â¦, n} with the property that fÌ(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), â¦, 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 rregular handicap distance antimagic graphs of order $n equiv 0 pmod{8}$ for all feasible values of r.
Interlace polynomials of friendship graphs
EubanksTurner, Christina ( Department of Mathematics, Loyola Marymount University, 90045 USA ) , Li, Aihua ( Department of Mathematical Sciences, Montclair State University, 07043 USA )
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
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In this paper, we study the interlace polynomials of friendship graphs, that is, graphs that satisfy the Friendship Theorem given by ErdÃ¶s, RÃ©nyi and Sos. Explicit formulas, special values and behavior of coefficients of these polynomials are provided. We also give the interlace polynomials of other similar graphs, such as, the butterfly graph.
On distance signless Laplacian spectrum and energy of graphs
Alhevaz, Abdollah ( Shahrood University of Technology ) , Baghipur, Maryam ( Shahrood University of Technology ) , Hashemi, Ebrahim ( Shahrood University of Technology )
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
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The distance signless Laplacian spectral radius of a connected graph G is the largest eigenvalue of the distance signless Laplacian matrix of Gâ, âdefined as âDâQ(G)â=âTr(G)â
+â
D(G)â, âwhere D(G) is the distance matrix of G and Tr(G) is the diagonal matrix of vertex transmissions of Gâ. âIn this paper we determine some upper and lower bounds on the distance signless Laplacian spectral radius of G based on its order and independence numberâ, âand characterize the extremal graphâ. âIn additionâ, âwe give an exact description of the distance signless Laplacian spectrum and the distance signless Laplacian energy of the join of regular graphs in terms of their adjacency spectrumâ.
The structure of graphs with forbidden induced $C_4$, $overline{C}_4$, $C_5$, $S_3$, chair and cochair
Ghazal, Salman ( Department of Mathematics,
Faculty of Sciences I, Lebanese University,
Beirut  Lebanon )
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
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We find the structure of graphs that have no C4, $overline{C}_4$, C5, S3, chair and cochair as induced subgraphs. Then we deduce the structure of the graphs having no induced C4, $overline{C_4}$, S3, chair and cochair 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.
Graphs, friends and acquaintances
Dalfo, Cristina ( Universitat Politecnica de Catalunya ) , Fiol, Miquel ÃƒÂ€ngel ( Universitat Politecnica de Catalunya )
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
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A graph is a mathematical object modeling the existence of a certain relation between pairs of elements of a given set. Many of the first results concerning graphs made reference to relationships between groups of people. In this article, we comment on four results of this kind: the Handshake lemma (related to graph colorings and Boolean algebra), a lemma on known and unknown people at a cocktail party (to Ramsey theory), a theorem on friends in common (to distanceregularity and coding theory), and Halls Marriage theorem (to the theory of networks). These four areas of graph theory, often with problems which are easy to state but difficult to solve, are extensively developed and currently give rise to much research work. As examples of representative problems and results of these areas we may cite the following: the Four Colors Theorem (4CTC), the Ramsey numbers, problems of the existence of distanceregular graphs and completely regular codes, and finally the study of topological proprieties of interconnection networks.
Color code techniques in rainbow connection
Septyanto, Fendy ( Departments of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia,
Depok, Indonesia ) , Sugeng, Kiki A. ( Departments of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia,
Depok, Indonesia )
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
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Let G be a graph with an edge kcoloring Î³ : E(G) â {1, â¦, k} (not necessarily proper). A path is called a rainbow path if all of its edges have different colors. The map Î³ is called a rainbow coloring if any two vertices can be connected by a rainbow path. The map Î³ is called a strong rainbow coloring if any two vertices can be connected by a rainbow geodesic. The smallest k for which there is a rainbow kcoloring (resp. strong rainbow kcoloring) on G is called the rainbow connection number (resp. strong rainbow connection number) of G, denoted rc(G) (resp. src(G)). In this paper we generalize the notion of âcolor codesâ that was originally used by Chartrand et al. in their study of the rc and src of complete bipartite graphs, so that it now applies to any connected graph. Using color codes, we prove a new class of lower bounds depending on the existence of sets with common neighbours. Tight examples are discussed, involving the amalgamation of complete graphs, generalized wheel graphs, and a special class of sequential join of graphs.
Domination number of the noncommuting graph of finite groups
Vatandoost, Ebrahim ( Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran ) , Khalili, Masoumeh ( Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran )
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
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Let G be a nonabelian group. The noncommuting graph of group G, shown by ÎG, is a graph with the vertex set G Z(G), where Z(G) is the center of group G. Also two distinct vertices of a and b are adjacent whenever ab â ba. A set S â V(Î) of vertices in a graph Î is a dominating set if every vertex v â V(Î) is an element of S or adjacent to an element of S. The domination number of a graph Î denoted by Î³(Î), is the minimum size of a dominating set of Î. </p><p>Here, we study some properties of the noncommuting graph of some finite groups. In this paper, we show that $gamma(Gamma_G)<frac{GZ(G)}{2}.$ Also we charactrize all of groups G of order n with t = â£Z(G)â£, in which $gamma(Gamma_{G})+gamma(overline{Gamma}_{G})in {nt+1,nt,nt1,nt2}.$
Parsimonious edgecoloring on surfaces
Belcastro, SarahMarie ( Mathematical Staircase, Inc., Holyoke MA, and Smith College, Northampton MA, U.S.A. )
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
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We correct a small error in a 1996 paper of Albertson and Haas, and extend their lower bound for the fraction of properly colorable edges of planar subcubic graphs that are simple, connected, bridgeless, and edgemaximal to other surface embeddings of subcubic graphs.
Characterization of perfect matching transitive graphs
Zhou, Ju ( Department of Mathematics
Kutztown University of Pennsylvania
Kutztown, PA 19530 USA )
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
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A graph G is perfect matching transitive, shortly PMtransitive, if for any two perfect matchings M and N of G, there is an automorphism fâ:âV(G)ââ¦âV(G) such that fe(M)â=âN, where fe(uv)â=âf(u)f(v). In this paper, the author proposed the definition of PMtransitive, verified PMtransitivity of some symmetric graphs, constructed several families of PMtransitive graphs which are neither vertextransitive nor edgetransitive, and discussed PMtransitivity of generalized Petersen graphs.
On total edge product cordial labeling of fullerenes
Baca, Martin ( Department of Applied Mathematics and Informatics, Technical University, Kosice, Slovak Republic ) , Irfan, Muhammad ( Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan ) , Javed, Aisha ( Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan ) , SemanicovaFenovcikova, Andrea ( Department of Applied Mathematics and Informatics, Technical University, Kosice, Slovak Republic )
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
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For a simple graph Gâ=â(V,âE) this paper deals with the existence of an edge labeling Ïâ:âE(G)âââ{0,â1,ââ¦,âkâ
ââ
1}, 2ââ¤âkââ¤ââ£E(G)â£, which induces a vertex labeling Ïâ
*â
â:âV(G)âââ{0,â1,ââ¦,âkâ
ââ
1} in such a way that for each vertex v, assigns the label $varphi(e_1)cdotvarphi(e_2)cdotldotscdot varphi(e_n) pmod k$, where e1,âe2,ââ¦,âen are the edges incident to the vertex v. The labeling Ï is called a ktotal edge product cordial labeling of G if â£(eÏ(i)â
+â
vÏâ
*â
(i))â
ââ
(eÏ(j)â
+â
vÏâ
*â
(j))â£ââ¤â1 for every i,âj, $0 le i < j le k1$, where eÏ(i) and vÏâ
*â
(i) is the number of edges and vertices with Ï(e)â=âi and Ïâ
*â
(v)â=âi, respectively. The paper examines the existence of such labelings for toroidal fullerenes and for Kleinbottle fullerenes.