Value-True Walks in Finite, Connected, Valuated Graphs.
Variable neighborhood search for extremal graphs. 17. Further conjectures and results about the index
The AutoGraphiX 2 system is used to compare the index of a connected graph G with a number of other graph theoretical invariants, i.e., chromatic number, maximum, minimum and average degree, diameter, radius, average distance, independence and domination numbers. In each case, best possible lower and upper bounds, in terms of the order of G, are sought for sums, differences, ratios and products of the index and another invariant. There are 72 cases altogether: in 7 cases known results were reproduced,...
Variations sur un algorithme de DANTZIG : application à la recherche des plus courts chemins dans les grands réseaux
Vertex Cyclic Graphs.
Vertex-disjoint stars in graphs
In this paper, we give a sufficient condition for a graph to contain vertex-disjoint stars of a given size. It is proved that if the minimum degree of the graph is at least k+t-1 and the order is at least (t+1)k + O(t²), then the graph contains k vertex-disjoint copies of a star . The condition on the minimum degree is sharp, and there is an example showing that the term O(t²) for the number of uncovered vertices is necessary in a sense.
Vertices contained in all minimum paired-dominating sets of a tree
A set of vertices in a graph is called a paired-dominating set if it dominates and contains at least one perfect matching. We characterize the set of vertices of a tree that are contained in all minimum paired-dominating sets of the tree.
Voltage graphs, group presentations and cages.