# Odd Graceful Labeling of Some New Graphs

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We performed a new kind of FCI study to get at the differences between what students believe and what they think scientists believe. Students took the FCI in the standard way, and then made a second pass indicating â€˜the answer they really believeâ€™ and â€˜the answer they think a...

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For the graph G1 and G2 the tensor product is denoted by G1(Tp)G2 which is the graph with vertex set V(G1(Tp)G2) = V(G1) Ã— V(G2) and edge set E(G1(Tp)G2) = {(u1, v1), (u2, v2)/u1u2ÏµE(G1) and v1v2ÏµE(G2)}. The graph Pm(Tp)Pn is disconnected for âˆ€m, n while the graphs Cm(Tp)Cn and...

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Given a binary matroid M on a set S and a pair of its elements (x, y), we obtain a new binary matroid Mx,y on S by using the splitting operation. In this paper, we examine the effect of the splitting operation on connected binary matroids. Conditions for this operation to preserve connectedness...

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We study the unique integrability of the center unstable subbundle of a codimension one dominated splitting.

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We study the dynamics of two-phase flow with gravity and point out three different transport mechanisms: non-cyclic advection, solenoidal advection, and gravity segregation. Each term has specific mathematical properties that can be exploited by specialized numerical methods. We argue that to...

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PairViz is an R package that produces orderings of statistical objects for visualization purposes. We abstract the ordering problem to one of constructing edge-traversals of (possibly weighted) graphs. PairViz implements various edge traversal algorithms which are based on Eulerian tours and...

- Further results on mean graphs. Vasuki, R.; Nagarajan, A. // Scientia Magna;2010, Vol. 6 Issue 3, p1
Let G(V, E) be a graph with p vertices and q edges. For every assignment f : V (G) ? {0; 1, 2, 3,ï¿½, q}, an induced edge labeling f* : E(G) ? {1, 2, 3 ï¿½, q} is defined by f*(uv) = {f(u)+f(v)/2, if f(u) and f(v) are of the same parity, f(u)+f(v)+1/2, otherwise. for every edge uv ? E(G)....

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- Splittings of free groups, normal forms and partitions of ends. Gadgil, Siddhartha; Pandit, Suhas // Proceedings of the Indian Academy of Sciences: Mathematical Scie;Apr2010, Vol. 120 Issue 2, p217
Splittings of a free group correspond to embedded spheres in the 3-manifold M = # S ï¿½ S. These can be represented in a normal form due to Hatcher. In this paper, we determine the normal form in terms of crossings of partitions of ends corresponding to normal spheres, using a graph of trees...