We prove that if G and H are primitive strongly regular graphs with the same parameters and φ is a homomorphism from G to H, then φ is either an isomorphism or a coloring (homomorphism to a complete subgraph). Moreover, any such coloring is optimal for G and its image is a maximum clique of H. Therefore, the only endomorphisms of a primitive strongly regular graph are automorphisms or colorings...

Mader (1985) proved that every strongly $k$-connected $n$-vertex digraph contains a strongly $k$-connected spanning subgraph with at most $2kn - 2k^2$ edges, and this is sharp. For dense strongly $k$-connected digraphs, the bound can be significantly improved for dense strongly $k$-connected digraphs. Let $\overline{\Delta}(D)$ be the maximum degree of the complement of the underlying undirecte...

We evaluate in closed form series of the type ∑ u(n)R(n), with (u(n))n a strongly B-multiplicative sequence and R(n) a (well-chosen) rational function. A typical example is: ∑ n>1 (−1)2 4n+ 1 2n(2n+ 1)(2n+ 2) = − 4 where s2(n) is the sum of the binary digits of the integer n. Furthermore closed formulas for series involving automatic sequences that are not strongly B-multiplicative, such as the...

We present a constant-factor approximation algorithm for computing an embedding of the shortest path metric of an unweighted graph into a tree, that minimizes the multiplicative distortion.

A binary moment diagram, which was proposed for arithmetic circuit verification, is a directed acyclic graph representing a function from binary-vectors to integers (f : {0, 1}n → Z). A multiplicative binary moment diagram is an extension of a binary moment diagram with edge weights attached. A multiplicative binary moment diagram can represent addition, multiplication and many other functions ...

We study the problem of exploring all nodes of an unknown directed graph. A searcher has to construct a tour that visits all nodes, but only has information about the parts of the graph it already visited. The goal is to minimize the cost of such a tour. In this paper, we present upper and lower bounds for both the deterministic and the randomized online version of exploring all nodes of direct...