Convex and Weakly Convex Domination in Prism Graphs

Open access

Abstract

For a given graph G = (V;E) and permutation π : VV the prism πG of G is defined as follows: VG) = V (G) ∪ V (G′), where G′ is a copy of G, and E(πG) = E(G) ∪ E(G′) ∪Mπ, where Mπ = {uv′ : uV (G); v = π (u)} and v′ denotes the copy of v in G′.

We study and compare the properties of convex and weakly convex dominating sets in prism graphs. In particular, we characterize prism γcon-fixers and -doublers. We also show that the differences γwcon(G) – γwcon(πG) and γwcon (πG) – 2γwcon (G) can be arbitrarily large, and that the convex domination number of πG cannot be bounded in terms of γcon (G).

[1] A.P. Burger, C.M. Mynhardt and W.D. Weakley, On the domination number of prisms of graphs, Discuss. Math. Graph Theory 2 (2004) 303–318. doi:10.7151/dmgt.1233

[2] G. Chartrand and F. Harary, Planar permutation graphs, Ann. Inst. Henri Poincare 3 (1967) 433–438.

[3] M. Lemańska and R. Zuazua, Convex universal fixers, Discuss. Math. Graph Theory 32 (2012) 807–812. doi:10.7151/dmgt.1631

[4] C.M. Mynhardt and Z. Xu, Domination in prisms of graphs: universal fixers, Util. Math. 78 (2009) 185–201.

[5] M. Rosicka, A proof of the universal fixer conjecture, Util. Math., to appear.

[6] K. Wash, Edgeless graphs are the only universal fixers, Czechoslovak Math. J. 64 (2014) 833–843. doi:10.1007/s10587-014-0136-3

Discussiones Mathematicae Graph Theory

The Journal of University of Zielona Góra

Journal Information


IMPACT FACTOR 2018: 0.741
5-year IMPACT FACTOR: 0.611



CiteScore 2018: 0.73

SCImago Journal Rank (SJR) 2018: 0.763
Source Normalized Impact per Paper (SNIP) 2018: 0.934

Mathematical Citation Quotient (MCQ) 2017: 0.36

Target Group

researchers in the fields of: colourings, partitions (general colourings), hereditary properties, independence and dominating structures (sets, paths, cycles, etc.), cycles, local properties, products of graphs

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 44 44 29
PDF Downloads 15 15 8