Showing papers in "AKCE International Journal of Graphs and Combinatorics in 2009"

TL;DR: In this paper, the authors survey a new type of labeling based on summation, the exclusive sum labeling, which is defined as the smallest number of isolated vertices that must be added to a graph H to achieve a sum graph, denoted by I(H).

TL;DR: In this article, it was shown that the planar grid Pm × Pn has a prime labeling if m ≤ n and n is a prime, where m is the number of vertices in the grid.

TL;DR: Polynomial algorithms for computing the cardinality of a minimum rooted secure set of trees are presented and an appropriate definition of such attacks and defenses is presented.

TL;DR: In this note, some of the open problems on various aspects of graph labelings which were posed by the participants during IWOGL 2009 and which have not been included in any of the other papers appearing in this volume are presented.

TL;DR: In this article, the authors survey the literature on the eccentricity sequence of a connected graph and make the following contribution: "The list of eccentricities of a graph G is the list of its eccentricities in non-increasing order".

TL;DR: The graph GP (n;k) with n and k relatively prime was introduced by Coxeter in (5), while the generalized Petersen graph GP was first considered in (6) and Castagna and Prins (3) completed the proof begun by Watkins in (8) that each generalized Pe- tersen graph is 3-edge-colorable as discussed by the authors.

TL;DR: In this article, the authors studied super (a,d)-vertex-antimagic total properties of disjoint union of paths, where the weight of a vertex is the sum of its label and the labels of all adjacent edges.

TL;DR: In this paper, two construction characterizations of defect n-extendable bipartite graphs and a necessary condition for minimal defect nextendability bipartitite graphs are presented.