let z2 = {0, 1} and g = (v ,e) be a graph. a labeling f : v → z2 induces an edge labeling f* : e →z2 defined by f*(uv) = f(u).f (v). for i ε z2 let vf (i) = v(i) = card{v ε v : f(v) = i} and ef (i) = e(i) = {e ε e : f*(e) = i}. a labeling f is said to be vertex-friendly if | v(0) − v(1) |≤ 1. the vertex balance index set is defined by {| ef (0) − ef (1) | : f is vertex-friendly}. in this paper ...

All graphs considered are finite and loopless, but may contain multiple edges. By a simple graph we shall mean a graph without multiple edges. It follows easily from a result of Mader [4, Theorem 1] that if G is a ^-connected simple graph of minimum degree at least k+2, then G contains a cycle C such that G-E(C) is ^-connected. Stronger results exist for the special case of 2-connected simple g...

We perform a systematic study in the computational complexity of the connected variant of three related transversal problems: Vertex Cover, Feedback Vertex Set, and Odd Cycle Transversal. Just like their original counterparts, these variants are NP-complete for general graphs. A graph G is H-free for some graph H if G contains no induced subgraph isomorphic to H . It is known that Connected Ver...

Let G be a 4-connected graph. For an edge e of G, we do the following operations on G: first, delete the edge e from G, resulting the graph G − e; second, for all the vertices x of degree 3 in G− e, delete x from G− e and then completely connect the 3 neighbors of x by a triangle. If multiple edges occur, we use single edges to replace them. The final resultant graph is denoted by G a e. If G a...

Let G (V, E) be a simple graph with vertex set V and edge set E. A generalized cycle is a subgraph such that any vertex degree is even. A simple cycle (briefly in a cycle) is a connected subgraph such that every vertex has degree 2. A basis of the cycle space is called a cycle basis of G (V, E). A cycle basis where the sum of the weights of the cycles is minimal is called a minimum cycle basis ...

We investigate generalizations of the following well-known problems in the framework of parameterized complexity: the feedback set problem and the cycle packing problem. Our problem setting is that we are given a graph and a vertex set S called “terminals”. Our purpose here is to consider the following problems: 1. The feedback set problem with respect to the terminals S. We call it the subset ...

mean labelings are a type of additive vertex labeling. this labeling assigns non-negative integers to the vertices of a graph in such a way that all edge-weights are different, where the weight of an edge is defined as the mean of the end-vertex labels rounded up to the nearest integer. in this paper we focus on mean labelings of some graphs that are the result of the corona operation. in parti...