An antimagic labeling of a connected graph with m edges is an injective assignment of labels from {1, . . . , m} to the edges such that the sums of incident labels are distinct at distinct vertices.â€¦ (More)

A card of a graph G is a subgraph formed by deleting one vertex. The Reconstruction Conjecture states that each graph with at least three vertices is determined by its multiset of cards. A dacardâ€¦ (More)

In a list (d1, . . . , dn) of positive integers, let r and s denote the largest and smallest entries. A list is gap-free if each integer between r and s is present. We prove that a gapfreeâ€¦ (More)

Inspired by a 1987 result of Hanson and Toft [Edge-colored saturated graphs, J. Graph Theory 11 (1987), 191â€“196] and several recent results, we consider the following saturation problem forâ€¦ (More)

Given the degree sequence d of a graph, the realization graph of d is the graph having as its vertices the labeled realizations of d, with two vertices adjacent if one realization may be obtainedâ€¦ (More)

A 2-switch is an edge addition/deletion operation that changes adjacencies in the graph while preserving the degree of each vertex. A well known result states that graphs with the same degreeâ€¦ (More)

We give characterizations of the structure and degree sequence of hereditary unigraphs, those graphs for which every induced subgraph is the unique realization of its degree sequence. The class ofâ€¦ (More)

Article history: Received 17 March 2011 Received in revised form 19 July 2011 Accepted 12 October 2011 Available online 15 October 2011 Communicated by M. Yamashita