In order to increase the paired-domination number of a graph G, minimum edges that must be subdivided (where each edge in G can no more than once) is called subdivision sdγpr(G) G. It well known sdγpr(G+e) smaller or larger for some e∉E(G). this note, we show that, if an isolated-free different from mK2, then, every e∉E(G), sdγpr(G+e)≤sdγpr(G)+2Δ(G).

A permutation graph is a cubic graph admitting a 1-factor M whose complement consists of two chordless cycles. Extending results of Ellingham and of Goldwasser and Zhang, we prove that if e is an edge of M such that every 4-cycle containing an edge of M contains e, then e is contained in a subdivision of the Petersen graph of a special type. In particular, if the graph is cyclically 5-edge-conn...

This report presents a particular implementation, and experiments on the Dividing Cubes algorithm whose the aim is to extract and display an iso-surface from a three-dimensional (3D) medical image. The regular subdivision of the voxels allows the projection of a subdivided voxel, on the raster image, to be at most equal to the size of a pixel. We optimize the subdivision parameters to get a com...

The aim of this paper is to present some odd graceful graphs. In particular we show that an odd graceful labeling of the all subdivision of double triangular snakes ( 2 k ∆ -snake ). We also prove that the all subdivision of 2 1 m∆ -snake are odd graceful. Finally, we generalize the above two results (the all subdivision of 2 k m∆ -snake are odd graceful).

Reverse subdivision aims at constructing a coarser representation of an object given by a fine polygon mesh. In this paper, we first derive a mask for reverse Loop subdivision that can be applied to both regular and extraordinary vertices. The mask is parameterized, and thus can also be used in reversing variants of Loop subdivision, such as those proposed by Warren and Litke. We apply this mas...

A set S of vertices of a graphG = (V,E) is a dominating set if every vertex of V (G)\S is adjacent to some vertex in S. The domination number γ(G) is the minimum cardinality of a dominating set of G. The domination subdivision number sdγ(G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the domination number. Velammal ...

In a graph G, a vertex dominates itself and its neighbors. A subset S ⊆ V (G) is a 2-dominating set of G if S dominates every vertex of V (G) \ S at least twice. The 2-domination number γ2(G) is the minimum cardinality of a 2-dominating set of G. The 2-domination subdivision number sdγ2(G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in ...

We show that an ’almost strong Lefschetz’ property holds for the barycentric subdivision of a shellable complex. From this we conclude that for the barycentric subdivision of a CohenMacaulay complex, the h-vector is unimodal, peaks in its middle degree (one of them if the dimension of the complex is even), and that its g-vector is an M -sequence. In particular, the (combinatorial) g-conjecture ...