We introduce a new class of subdivision surfaces which generalize uniform tensor product B-spline surfaces of any bi-degree to meshes of arbitrary topology. Surprisingly , this can be done using subdivision rules that involve direct neighbors only. Consequently, our schemes are very easy to implement, regardless of degree. The famous Catmull-Clark scheme is a special case. Similarly we show tha...

In this study, the explicit expressions for F-index and coindex of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph (line graph of the subdivision graph) are obtained.

In [2, 3, 20, 21] the authors explored a construction to produce multiresolutions from given subdivisions. Certain assumptions carried through that work, two of which we wish to challenge: (1) that multiresolutions for irregular meshes have to be constructed on the fly rather than being prepared beforehand and (2) that the connectivity graph of the coarse mesh would have to be a subgraph of the...

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).

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...

Mader asked whether every C4-free graph G contains a subdivision of a complete graph whose order is at least linear in the average degree of G. We show that there is a subdivision of a complete graph whose order is almost linear. More generally, we prove that every Ks,t-free graph of average degree r contains a subdivision of a complete graph of order r 1 2 + 1 2(s−1).