we define minimal cn-dominating graph $mathbf {mcn}(g)$, commonality minimal cn-dominating graph $mathbf {cmcn}(g)$ and vertex minimal cn-dominating graph $mathbf {m_{v}cn}(g)$, characterizations are given for graph $g$ for which the newly defined graphs are connected. further serval new results are developed relating to these graphs.

The medial axis of a plane domain is deened to be the set of the centers of the maximal inscribed disks. It is essentially the cut loci of the inward unit normal bundle of the boundary. We prove that if a plane domain has nite number of boundary curves each of which consists of nite number of real analytic pieces, then the medial axis is a connected geometric graph in R 2 with nitely many verti...

This paper presents a new algorithm for reducing the minimal surface bias associated with volumetric graph cuts for 3D reconstruction from multiple calibrated images. The algorithm is based on an iterative graph-cut over narrow bands combined with an accurate surface normal estimation. At each iteration, we first optimize the normal to each surface patch in order to obtain a precise value for t...

An interval graph is the intersection graph of a finite set of intervals on a line and a circular-arc graph is the intersection graph of a finite set of arcs on a circle. While a forbidden induced subgraph characterization of interval graphs was found fifty years ago, finding an analogous characterization for circular-arc graphs is a long-standing open problem. In this work, we study the inters...

For a positive integer s, a graph Γ is called s-arc transitive if its full automorphism group AutΓ acts transitively on the set of s-arcs of Γ . Given a group G and a subset S of G with S = S−1 and 1 / ∈ S, let Γ = Cay(G, S) be the Cayley graph of G with respect to S and G R the set of right translations of G on G. Then G R forms a regular subgroup of AutΓ . A Cayley graph Γ = Cay(G, S) is call...

In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and  the icosahedral graph.

We propose a graphical implementation for (possibly recursive) processes of the π-calculus, encoding each process into a graph. Our implementation is sound and complete with respect to the structural congruence for the calculus: Two processes are equivalent if and only if they are mapped into graphs with the same normal form. Most importantly, the encoding allows the use of standard graph rewri...

a signed graph (marked graph) is an ordered pair $s=(g,sigma)$$(s=(g,mu))$, where $g=(v,e)$ is a graph called the underlyinggraph of $s$ and $sigma:erightarrow{+,-}$$(mu:vrightarrow{+,-})$ is a function. for a graph $g$, $v(g),e(g)$ and $c(g)$ denote its vertex set, edge set and cut-vertexset, respectively. the lict graph $l_{c}(g)$ of a graph $g=(v,e)$is defined as the graph having vertex set ...

A graph is normal if there exists a cross-intersecting pair of set families one of which consists of cliques while the other one consists of stable sets, and furthermore every vertex is obtained as one of these intersections. It is known that perfect graphs are normal while Cs, CT. and (_: are not. We conjecture that these three graphs are the only minimally not normal graphs. We give sufficien...