We consider the connected variant of the classic mixed search game where, in each search step, cleaned edges form a connected subgraph. We consider graph classes with bounded connected monotone mixed search number and we deal with the the question weather the obstruction set, with respect of the contraction partial ordering, for those classes is finite. In general, there is no guarantee that th...

We study entanglement properties of mixed density matrices obtained from combinatorial laplacian matrices of graphs. We observe that some classes of graphs give arise to entangled (separable) states independently of their labelings. MSC2000: 05C50; PACS numbers: 03.67.-a, 03.67.-Mn

We show that the mixed search number and the linear-width of interval graphs and of split graphs can be computed in linear time and in polynomial time, respectively.

the first ($pi_1$) and the second $(pi_2$) multiplicative zagreb indices of a connected graph $g$, with vertex set $v(g)$ and edge set $e(g)$, are defined as $pi_1(g) = prod_{u in v(g)} {d_u}^2$ and $pi_2(g) = prod_{uv in e(g)} {d_u}d_{v}$, respectively, where ${d_u}$ denotes the degree of the vertex $u$. in this paper we present a simple approach to order these indices for connected graphs on ...

It is well-known that the Chinese Postman Problem on undirected and directed graphs is polynomial-time solvable. We extend this result to edge-colored multigraphs. Our result is in sharp contrast to the Chinese Postman Problem on mixed graphs, i.e., graphs with directed and undirected edges, for which the problem is NP-hard.