Families of ICIS with constant total Milnor number

Milnor Number of Weighted-Lê–Yomdin Singularities

The total-chromatic number of some families of snarks

The total chromatic number χ T (G) is the least number of colours needed to colour the vertices and edges of a graph G, such that no incident or adjacent elements (vertices or edges) receive the same colour. It is known that the problem of determining the total chromatic number is NP-hard and it remains NP-hard even for cubic bipartite graphs. Snarks are simple connected bridgeless cubic graphs...

DOMINATION NUMBER OF TOTAL GRAPH OF MODULE

 Let $R$ be a commutative ring and $M$ be an $R$-module with $T(M)$ as subset, the set of torsion elements. The total graph of the module denoted by $T(Gamma(M))$, is the (undirected) graph with all elements of $M$ as vertices, and for distinct elements $n,m in M$, the vertices $n$ and $m$ are adjacent if and only if $n+m in T(M)$. In this paper we study the domination number of $T(Gamma(M))$ a...

Sequences with constant number of return words

An infinite word has the property Rm if every factor has exactly m return words. Vuillon showed that R2 characterizes Sturmian words. We prove that a word satisfies Rm if its complexity function is (m − 1)n + 1 and if it contains no weak bispecial factor. These conditions are necessary for m = 3, whereas for m = 4 the complexity function need not be 3n + 1. A new class of words satisfying Rm is...

Passive Total Systems with Constant Coefficients.

where YO has arbitrary constants for elements. T.he system composed of (1) and (3), if passive, is known to have a unique solution in the set of analytic functions by a general theorem of Konig1 and the linearity of the right members makes possible the immediate extension of this result to the set of once differentiable functions (say, by the method of successive approximations). Recently, Vess...