双三角蛇图调和标号.pdfVIP

On harmonious labelings of the double triangular snake ∗ Xi Yue Yang Yuansheng Xu Xirong Department of Computer Science Dalian University of Technology Dalian, 116024, P. R. China e-mail: yangys@ Khandoker Mohammed Mominul Haque Department of Computer Science and Engineering Shahjalal University of Science and Technology Sylhet-3114 , Bangladesh Abstract A triangular snake has been defined as a connected graph in which all blocks are tri- angles and the block-cut point graph is a path. David Moulton proved that triangular snakes with p triangles are graceful if p is congruent to 0 or 1 modulo 4. Xu proved that they are harmonious if and only if p is congruent to 0, 1 or 3 modulo 4. A double triangular snake is a graph formed by two triangular snakes have a common path. In this paper, we prove that all double triangular snakes are harmonious. Keywords: harmonious graph, triangular snake, vertex labeling, edge labeling 1 Introduction In 1980 Graham and Sloane [3] gave a variation on graceful labeling of graphs. A simple,finite graph G with n vertices and q (≥ n) edges is said to be harmonious if there is an injection f : V (G) → Z , Z is the integer group modulo q, such that the induced function q q g : E (G) → Zq defined by g (xy)=[f (x) + f (y)] mod q , x, y ∈ V (G) is a bijection. Such a labeling of the vertices and edges is called a harmonious labeling of graph. In a harmonious This research is support