We introduce new labeling called m-bonacci graceful labeling. A graph G on n edges is if the vertices can be labeled with distinct integers from set {0,1,2,…,Zn,m} such that derived edge labels are first numbers. show complete graphs, bipartite gear triangular grid and wheel graphs not graceful. Almost all trees give to cycles, friendship polygonal snake double graphs.

Answering a question posed by Joseph Malkevitch, we prove that there exists polyhedral graph, with triangular faces, such every realization of it as the graph convex polyhedron includes at least one face is scalene triangle. Our construction based on Kleetopes, and shows an integer $i$ all $i$-iterated Kleetopes have face. However, also show triangulated graphs non-convex non-self-crossing real...

Many data structures are possible for the storage of topological information for computer-based maps. The PAN graph is here suggested as an aid in the selection of a strategy appropriate to the application. Examples are given for the mapping of triangular networks and Thiessen polygons. Application of the technique is appropriate to both education in, and design of, spatial data structures for ...

Let a1, a2, . . . , ak be positive integers. An (a1, a2, . . . , ak)-packing coloring of a graph G is a mapping from V (G) to {1, 2, . . . , k} such that vertices with color i have pairwise distance greater than ai. In this paper, we study (a1, a2, . . . , ak)packing colorings of several lattices including the infinite square, triangular, and hexagonal lattices. For k small, we determine all ai...

Given a graph G = (V,E) and a proper vertex colouring of G, a Kempe chain is a subset of V that induces a maximal connected subgraph of G in which every vertex has one of two colours. To make a Kempe change is to obtain one colouring from another by exchanging the colours of vertices in a Kempe chain. Two colourings are Kempe equivalent if each can be obtained from the other by a series of Kemp...

A biclique is a maximal induced complete bipartite subgraph of a graph. We investigate the intersection structure of edge-sets of bicliques in a graph. Specifically, we study the associated edge-biclique hypergraph whose hyperedges are precisely the edge-sets of all bicliques. We characterize graphs whose edgebiclique hypergraph is conformal (i.e., it is the clique hypergraph of its 2-section) ...

The first part of our paper presents a composite programmable graph grammar model for the self-adaptive two dimensional hp Finite Element Method algorithms (2D hp-FEM) with mixed triangular and rectangular finite elements. The two dimensional model is a starting point for the three dimensional model of self-adaptive hp-FEM presented in the second part of this paper. A computational mesh is repr...

A novel method for surface reconstruction from an unorganized point set is presented. An energy functional based on a weighted minimal surface model is proposed for surface reconstruction, which is efficiently minimized by graph cut methods. By solving the minimization problem on the graph dual to a Delaunaybased tetrahedral mesh, the advantages of explicit and implicit methods for surface reco...