6 research outputs found
A note on the convexity number for complementary prisms
In the geodetic convexity, a set of vertices of a graph is
if all vertices belonging to any shortest path between two
vertices of lie in . The cardinality of a maximum proper convex
set of is the of . The
of a graph arises from the
disjoint union of the graph and by adding the edges of a
perfect matching between the corresponding vertices of and .
In this work, we we prove that the decision problem related to the convexity
number is NP-complete even restricted to complementary prisms, we determine
when is disconnected or is a cograph, and we
present a lower bound when .Comment: 10 pages, 2 figure
Minimum Weight Dynamo and Fast Opinion Spreading
We consider the following multi--level opinion spreading model on networks. Initially, each node gets a weight from the set , where such a weight stands for the individuals conviction of a new idea or product.
Then, by proceeding to rounds, each node updates its weight according to the weights of its neighbors.
We are interested in the initial assignments of weights leading each node to get the value
--e.g. unanimous maximum level acceptance-- within
a given number of rounds.
We determine lower bounds on the sum of the initial weights of the nodes under the irreversible simple majority rules,
where a node increases its weight if and only if the majority of its neighbors have a weight that is higher than its own one. Moreover, we provide constructive tight upper bounds for some class of regular topologies: rings, tori, and cliques
Minimum weight dynamo and fast opinion spreading
We consider the following multi–level opinion spreading model on networks. Initially, each node gets a weight from the set {0,…,k − 1}, where such a weight stands for the individuals conviction of a new idea or product. Then, by proceeding to rounds, each node updates its weight according to the weights of its neighbors. We are interested in the initial assignments of weights leading each node to get the value k − 1 –e.g. unanimous maximum level acceptance– within a given number of rounds. We determine lower bounds on the sum of the initial weights of the nodes under the irreversible simple majority rules, where a node increases its weight if and only if the majority of its neighbors have a weight that is higher than its own one. Moreover, we provide constructive tight upper bounds for some class of regular topologies: rings, tori, and cliques
Minimum Weight Dynamo and Fast Opinion Spreading
We consider the following multi–level opinion spreading model in networks. Initially, each node gets a weight from the set {0, ..., k − 1}; where the weight of a node tells how much the actor, represented by the node, is convinced of the new idea (or product). Then, the process proceeds in rounds; during each round each node updates its weight depending on the weights of its neighbors.
We are interested in the initial assignments of weights leading each node to get the value k − 1 –e.g. unanimous maximum level acceptance– within a given number of rounds. We determine lower bounds on the sum of the initial weights of the nodes under the irreversible simple majority rules, where a node increases its weight if and only if the majority of its neighbors have a weight that is higher than its own one. Moreover, we provide constructive tight upper bounds for some class of regular topologies: rings, tori, and cliques