A block graph is a graph whose blocks are cliques. A block duplicate (BD) graph is a graph obtained by adding true twins (i.e., adjacent vertices with the same closed neighborhood...
Let G be a planar embedded 2-connected graph. Then the vertices of its resonance graph R(G) are the 1-factors of G, two 1-factors being adjacent whenever their symmetric differenc...
In the Connected Dominating Set problem we are given as input a graph G and a positive integer k, and are asked if there is a set S of at most k vertices of G such that S is a dom...
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...
Let ^G be a graph obtained from a graph G with no loops or coloops by replacing each edge e = uw of G by a connected graph He that has only the vertices u and w in common with the...