Electronic Journal of Graph Theory and Applications  

Andrew Bowling,Ping Zhang

A zonal labeling of a plane graph G is an assignment of the two nonzero elements of the ring Z3 of integers modulo 3 to the vertices of G such that the sum of the labels of the vertices on the boundary of each regio... see more

Jose Maria P Balmaceda,Dom Vito A Briones

Association schemes on triples (ASTs) are ternary analogues of classical association schemes, whose relations and adjacency algebras are ternary instead of binary. We provide a survey of the current progress in the study of ASTs, highlighting open questio... see more

Kiki A. Sugeng,Peter John,Michelle L. Lawrence,Lenny F. Anwar,Martin Baca,Andrea Semanicová-Fenovcíková

Let G = (V(G),E(G)) be a graph with the nonempty vertex set V(G) and the edge set E(G). Let Zn be the group of integers modulo n and let k be a positive integer. A modular irregular labeling of a grap... see more

Ioan Tomescu

In this paper, the vertex-degree function index Hf(G) is considered when function f(x) belongs to four classes of functions determined by the following properties: strictly convex versus strictly concave and strictly increasing versus ... see more

Yeva Fadhilah Ashari,A.N.M. Salman,Rinovia Simanjuntak,Andrea Semanicová-Fenovcíková,Martin Baca

A simple graph G(V, E) admits an H-covering if every edge in G belongs to a subgraph of G isomorphic to H. In this case, G is called H-magic if there exists a bijective function f : V ? E ? {1, 2... see more

Pannawat Eakawinrujee,Nantapath Trakultraipruk

A paired dominating set of a graph G is a dominating set whose induced subgraph has a perfect matching. The paired domination number ?pr(G) of G is the minimum cardinality of a paired dominating set. A paired dominating set&n... see more

Bryan Freyberg,Melissa Keranen

Lorenzo Federico

We introduce a model for inhomogeneous random graphs designed to have a lot of flexibility in the assignment of the degree sequence and the individual edge probabilities while remaining tractable. To achieve this we run a Poisson point process over the sq... see more

Risma Yulina Wulandari,Rinovia Simanjuntak

A graph G is distance antimagic if there is a bijection f : V(G)?{1, 2, …, |V(G)|} such that for every pair of distinct vertices x and y applies w(x)?w(y), where w(x)=S z ? N(x)f(z) and N(x)... see more

Tomáš Vetrík

Among bipartite graphs with given order and matching number/vertex cover number/edge cover number/independence number, among multipartite graphs with given order, and among graphs with given order and chromatic number, we present the graphs having the max... see more

Rian Febrian Umbara,A.N.M. Salman,Pritta Etriana Putri

A rainbow path in an edge-colored graph G is a path that every two edges have different colors. The minimum number of colors needed to color the edges of G such that every two distinct vertices are connected by a rainbow path is called... see more

Hilda Assiyatun,Maya Nabila,Edy Tri Baskoro

Let F, G and H be any simple graphs. The notation F ? (G, H) means for any red-blue coloring on the edges of graph F, there exists either a red copy of G or a blue copy of H. If F ? (G, H), then graph... see more

Zhiguo Li,Qing Ye,Zeling Shao

The Alon-Tarsi number AT(G) of a graph G is the least k for which there is an orientation D of G with max outdegree k - 1 such that the number of spanning Eulerian subgraphs of G w... see more

Jyoti Champanerkar,Aihua Li

In this paper, we study the interlace polynomial of a special graph with n vertices, called 4n-snowflake graph. It is similar as the friendship graph Fn of n vertices, which is made of n 3-cycles sharing one ce... see more

Cristina Dalfo,Miquel Àngel Fiol

A Moore (r, z, k)-mixed graph G has every vertex with undirected degree r, directed in- and out-degree z, diameter k, and number of vertices (or order) attaining the corresponding Moore bound M(r, z, k) for mixed gr... see more

Mostafa Tavakoli,Meysam Korivand,Ahmad Erfanian,Gholamreza Abrishami,Edy Tri Baskoro

For an ordered subset S = {v1, …, vk} of vertices in a connected graph G and an edge e' of G, the edge metric S-representation of e'=ab is the vector rGe(e'|S)=(dG(e',v1),…,dG(e',vk)) , where dG(... see more

Dian Eka Wijayanti,Noor Hidayat,Diari Indriati,Abdul Rouf Alghofari,Slamin Slamin

A distance vertex irregular total k-labeling of a simple undirected graph G = G(V, E), is a function f : V(G)?E(G)?{1, 2, …, k} such that for every pair vertices u, v ? V(G) and u ? v, the weights of u and ... see more

Kanagasabapathi Somasundaram,Jayabalan Geetha,Radhakrishnan Vignesh

Luis A. Dupont,Daniel G. Mendoza,Miriam Rodriguez

Let G be a finite group. The enhanced power graph GGe of G is the graph with vertex set G and two distinct vertices are adjacent if they generate a cyclic subgroup of G. In this article, we calculate the rainbow con... see more

Mahsa Mozafari-Nia,Moharram N. Iradmusa

A vi-simultaneous proper k-coloring of a graph G is a coloring of all vertices and incidences of the graph in which any two adjacent or incident elements in the set V(G)?I(G) receive distinct colors, where I(G) is t... see more

Fawwaz Fakhrurrozi Hadiputra,Eunike Setiawan,Tita Khalis Maryati,Denny Riama Silaban

Let G = (V, E) be a simple undirected graph. A labeling f : V(G)?{1, …, k} is a local inclusive d-distance vertex irregular labeling of G if every adjacent vertices x, y ? V(G) have distinct weights, with the w... see more

Grace Aspenson,Dustin Baker,Bryan Freyberg,Coy Schwieder

Other than C9 there are 239 connected unicyclic graphs with exactly 9 edges. We use established graph labeling results to prove that every one of them decomposes the complete graph Kn if n = 0 or 1 (mod 18).

Zeling Shao,Yanling Hu,Huiru Geng,Zhiguo Li

The book embedding of a graph G is to arrange the set of points of the graph on a line (spine) and embed the edges on the half-plane bounded by the spine so that the edges in the same page do not intersect with each other. If the maxim... see more

Alan Bonhert,Luke Branson,Patrick Joseph Otto

We use Rosa-type labelings to decompose complete graphs into unicyclic, disconnected, bipartite graphs on nine edges – namely, those featuring cyclic component C4, C6, or C8. For any such graph H, we prove there exists an H-design... see more