The vertex arboricity ρ(G) of a graph G is the minimum number of subsets into which the vertex set V (G) can be partitioned so that each subset induces an acyclic graph. In this paper, it is shown that if G is a toroidal graph without 7-cycles, moreover, G contains no triangular and adjacent 4-cycles, then ρ(G) ≤ 2. Mathematics Subject Classification: Primary: 05C15; Secondary: 05C70

The adjacent vertex-distinguishing proper edge-coloring is the minimum number of colors required for a G, in which no two vertices are incident to edges colored with same set colors. an G called edge-chromatic index. In this paper, I compute index Anti-prism, sunflower graph, double triangular winged prism, rectangular prism and Polygonal snake graph.

In this article, we consider the NP-hard problem of two-step colouring a graph. It is required to colour graph in given number colours way, when no pair vertices has same colour, if these are at distance 1 or 2 between each other. The optimum one that uses minimum possible colours.The studied application grid graphs. We four types grids: triangular, square, hexagonal, and octogonal. show hexago...

The main focus of this work is to obtain upper bounds on the weighted chromatic number of some classes of graphs in terms of the weighted clique number. We first propose an 11 6 -approximation algorithm for multicoloring any weighted planar graph. We then study the multicoloring problem on powers of square and triangular meshes. Among other results, we show that the infinite triangular mesh is ...

By finding explicit PD-sets we show that permutation decoding can be used for the binary code obtained from an adjacency matrix of the triangular graph T (n) for any n ≥ 5.

We establish new lower and upper bounds for the real number graph labelling problem. As an application, we completely determine the optimum spans of L(p, q)-labellings of the infinite triangular plane lattice (solving an open problem of Griggs).

An interesting connection between graph homomorphisms to odd cycles and circular chromatic number is presented. By using this connection, bounds for circular chromatic number of triangle-free hexagonal graphs (i.e. induced subgraphs of triangular lattice) are given.

The ladder graph plays an important role in many applications as Electronics, Electrical and Wireless communication areas. The aim of this work is to present a new class of odd graceful labeling for the ladder graph. In particular, we show that the ladder graph Ln with m-pendant Ln mk1 is odd graceful. We also show that the subdivision of ladder graph Ln with m-pendant S(Ln)  mk1 is odd grace...

In this technical report we study different parallel graph coloring algorithms and their application to the incomplete-LU factorization. We implement graph coloring based on different heuristics and showcase their performance on the GPU. We also present a comprehensive comparison of level-scheduling and graph coloring approaches for the incomplete-LU factorization and triangular solve. We discu...