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On the Signed (Total) K-Independence Number in Graphs

Abdollah Khodkar;  Babak Samadi;  Lutz Volkmann — 2015

Discussiones Mathematicae Graph Theory

Let G be a graph. A function f : V (G) → {−1, 1} is a signed k- independence function if the sum of its function values over any closed neighborhood is at most k − 1, where k ≥ 2. The signed k-independence number of G is the maximum weight of a signed k-independence function of G. Similarly, the signed total k-independence number of G is the maximum weight of a signed total k-independence function of G. In this paper, we present new bounds on these two parameters which improve some existing bounds....

New Bounds on the Signed Total Domination Number of Graphs

Seyyed Mehdi Hosseini Moghaddam;  Doost Ali Mojdeh;  Babak Samadi;  Lutz Volkmann — 2016

Discussiones Mathematicae Graph Theory

In this paper, we study the signed total domination number in graphs and present new sharp lower and upper bounds for this parameter. For example by making use of the classic theorem of Turán [8], we present a sharp lower bound on Kr+1-free graphs for r ≥ 2. Applying the concept of total limited packing we bound the signed total domination number of G with δ(G) ≥ 3 from above by [...] . Also, we prove that γst(T) ≤ n − 2(s − s′) for any tree T of order n, with s support vertices and s′ support vertices...

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