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 paper we study several problems concerning the number of homomorphisms of trees. We begin with an algorithm for the number of homomorphisms from a tree to any graph. By using this algorithm and some transformations on trees, we study various extremal problems about the number of homomorphisms of trees. These applications include a far reaching generalization and a dual of Bollobás and T...

The Gesture Pendant, a computer vision system worn as a piece of jewelry, allows the wearer to control electronic devices in the environment through simple hand gestures. Gestures provide an advantage over traditional device interfaces (such as remote controls) in that they are easily used by all people, including those with such disabilities as loss of vision, motor skills, and mobility. The G...

For a connected graph G of order n, a subset S of vertices of G is a monophonic set of G if each vertex v in G lies on a x-y monophonic path for some elements x and y in S. The minimum cardinality of a monophonic set of G is defined as the monophonic number of G, denoted by m(G). A monophonic set of cardinality m(G) is called a m–set of G. A set S of vertices of a connected graph G is an open m...

A bstract The string vertices of closed field theory are subsets the moduli spaces punctured Riemann surfaces that satisfy a geometric version Batalin-Vilkovisky master equation. We present homological proof existence and their uniqueness up to canonical transformations. Using hyperbolic metrics on with geodesic boundaries we give an exact construction as sets systole greater than or equal L ≤ ...

Abstract A graph $H$ is common if the number of monochromatic copies in a 2-edge-colouring complete $K_n$ asymptotically minimised by random colouring. Burr and Rosta, extending famous conjecture Erdős, conjectured that every common. The conjectures Erdős Rosta were disproved Thomason Sidorenko, respectively, late 1980s. Collecting new examples graphs had not seen much progress since then, alth...

Polyurethane (PU) homopolymers and PU/polystyrene (PS) interpenetrating polymer networks (IPNs) were successfully synthesized changing the length of the pendant poly(ethylene oxide) (PEO) chains and the grafting density of PEO chains. All the PU/PS IPNs had the microphase-separated structures in which the PS-rich phase domains were dispersed in the matrix of the PU-rich phase. The domain size d...