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On the inverse signed total domination number in graphs

Mojdeh D. A., Samadi B.

Opuscula Mathematica

2017

Vol. 37, no. 3

447--456

In this paper, we study the inverse signed total domination number in graphs and present new sharp lower and upper bounds on this parameter. For example by making use of the classic theorem of Turán (1941), we present a sharp upper bound on Kr+1-free graphs for r ≥ 2. Also, we bound this parameter for a tree from below in terms of its order and the number of leaves and characterize all trees attaining this bound.

Total limited packing in graphs

Hosseini Moghaddam S. M., Mojdeh D. A., Samadi B.

Fasciculi Mathematici

2016

Nr 56

121--127

We define a k-total limited packing number in a graph, which generalizes the concept of open packing number in graphs, and give several bounds on it. These bounds involve many well known parameters of graphs. Also, we establish a connection among the concepts of tuple domination, tuple total domination and total limited packing that implies some results.