Electronic Journal of Graph Theory and Applications  

Nikson Simarmata,Ikhlas Pratama Sandy,Kiki A. Sugeng

In 1967, Rosa introduced ß - labeling which was then popularized by Golomb under the name graceful. Graceful labeling on a graph G is an injective function f : V(G)?{0, 1, 2, …, |E(G)|} such that, when each edge uv ? E(G... see more

Frances Dean,Max Everett,Ralph Morrison

The divisorial gonality of a graph is the minimum degree of a positive rank divisor on that graph. We introduce the multiplicity-free gonality of a graph, which restricts our consideration to divisors that place at most 1 chip on each vertex. We... see more

Jabulani Phakathi,Yevhen Zelenyuk,Yuliya Zelenyuk

Let G be a finite group and let r ? N. An r-coloring of G is any mapping ? : G ? {1, …, r}. A coloring ? is symmetric if there is g ? G such that ?(gx-1g)=?(x) for every ... see more

Kshittiz Chettri,Biswajit Deb,Anjan Gautam

Let S = (G, s) be a balanced and canonically consistent signed graph. The 2-path signed graph S#S = (G2, s') of S has the underlying graph as G2 and the sign s'(uv) of an edge uv in it is -1... see more

Mehrdad Nasernejad

Suppose that V = {1, …, n} is a non-empty set of n elements, S = {S1, …, Sm} a non-empty set of m non-empty subsets of V. In this paper, by using some algebraic notions in commutative algebra, we investigate th... see more

Trung Duy Doan,Le Thi Duyen

Let G be an edge-coloured connected graph G. A path P in the graph G is called l-rainbow path if each subpath of length at most l + 1 is rainbow. The graph G is called (k, l)-rainbow connect... see more

Ryo Uchiumi

For a graph with edge ordering, a linear order on the edge set, we obtain a permutation of vertices by considering the edges as transpositions of endvertices. It is known from Dénes’ results that the permutation of a tree is a full cyclic for any edge ord... see more

Joshua Lambert,Michael Tiemeyer

Let K = K(a, p; ?1, ?2) be the multigraph with: the number of parts equal to p; the number of vertices in each part equal to a; the number of edges joining any two vertices of the same part equal to ?1; and the number of edges joi... see more

Muhammad Ridwan,Hilda Assiyatun,Edy Tri Baskoro

For every graph G, the dominating partition dimension of G is either the same as its partition dimension or one higher than its partition dimension. In this paper, we consider some general connections among these three graph parameters: par... see more

Djoko Suprijanto

Michal Staš,Juraj Valiska

The crossing number cr(G) of a graph G is the minimum number of edge crossings over all drawings of G in the plane, and the optimal drawing of G is any drawing at which the desired minimum number of crossings is ach... see more

Alex Ralph Baisa Nieva,Karen P. Nocum

In this paper, we find a special type of non-traceable cubic bridge graph called well-formed graph whose central fragment is isomorphic to a hairy cycle and whose branches are pairwise isomorphic. We then show that a well-formed graph can be par... see more

Nobuaki Obata

We derive a formula for the QE constant of a complete multipartite graph and determine the complete multipartite graphs of non-QE class, namely, those which do not admit quadratic embeddings in Euclidean spaces. Moreover, we prove that there are exactly f... see more