We describe an algorithm to compute the Tutte polynomial of large fragments of Archimedean tilings by squares, triangles, hexagons and combinations thereof. Our algorithm improves a well known method… Expand

This paper deals with the maximum value of the difference between the determining number and the metric dimension of a graph as a function of its order. Our technique requires to use… Expand

We introduce a new property of graphs called 'q-state Potts uniqueness' and relate it to chromatic and Tutte uniqueness, and also to 'chromatic-flow uniqueness', recently studied by Duan, Wu and Yu.Expand

A set of vertices S in a graph G is a resolving set for G if, for any two vertices u,v, there exists [email protected]?S such that the distances d(u,x) d(v,x).Expand

We provide new proofs and results on the determining number of trees and Cartesian products of graphs and establish some lower bounds on the difference between the two parameters.Expand

We give a new method of generating strongly polynomial sequences of graphs, i.e.,?sequences ( H k ) indexed by a tuple k = ( k 1 , ? , k h ) of positive integers, with the property that, for each fixed graph G , the number of homomorphisms from G to H k is given by the evaluation p ( G) .Expand