580 research outputs found
3-Factor-criticality in double domination edge critical graphs
A vertex subset of a graph is a double dominating set of if
for each vertex of , where is the set of the
vertex and vertices adjacent to . The double domination number of ,
denoted by , is the cardinality of a smallest double
dominating set of . A graph is said to be double domination edge
critical if for any edge . A double domination edge critical graph with is called --critical. A graph is
-factor-critical if has a perfect matching for each set of
vertices in . In this paper we show that is 3-factor-critical if is
a 3-connected claw-free --critical graph of odd order
with minimum degree at least 4 except a family of graphs.Comment: 14 page
Distances and Domination in Graphs
This book presents a compendium of the 10 articles published in the recent Special Issue “Distance and Domination in Graphs”. The works appearing herein deal with several topics on graph theory that relate to the metric and dominating properties of graphs. The topics of the gathered publications deal with some new open lines of investigations that cover not only graphs, but also digraphs. Different variations in dominating sets or resolving sets are appearing, and a review on some networks’ curvatures is also present
Characterizing Heterogeneity in Cooperative Networks From a Resource Distribution View-Point
© by International Press. First published in Communications in Information and Systems, Vol. 14, no. 1, 2014, by International Press.DOI: http://dx.doi.org/10.4310/CIS.2014.v14.n1.a1A network of agents in which agents with a diverse set of resources
or capabilities interact and coordinate with each other to accomplish various tasks constitutes a heterogeneous cooperative network. In this paper, we investigate heterogeneity in terms of resources allocated to agents within the network. The objective is to distribute resources in such a way that every agent in the network
should be able to utilize all these resources through local interactions. In particular, we formulate a graph coloring problem in which
each node is assigned a subset of labels from a labeling set, and a graph is considered to be completely heterogeneous whenever all the labels in the labeling set are available in the closed neighborhood of every node. The total number of different resources that can be accommodated within a system under this setting depends
on the underlying graph structure of the network. This paper provides an analysis of the assignment of multiple resources to nodes and the effect of these assignments on the overall heterogeneity of the network
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