A general method for proving comparison principles for Hamilton-Jacobi equations on networks is introduced. It consists in constructing a vertex test function to be used in the doubling variable technique. The first important consequence is that it provides very general existence and uniqueness results for Hamilton-Jacobi equations on networks with Hamiltonians that are not convex with respect ...

The matrix element of the electromagnetic current between pion states is calculated in quenched lattice QCD at a temperature of T = 0.93 T c. The nonperturbatively improved Sheikholeslami-Wohlert action is used together with the corresponding O(a) improved vector current. The electromagnetic vertex function is extracted for pion masses down to 360 MeV and momentum transfers Q 2 ≤ 2.7 GeV

The high temperature limit of the 3-graviton vertex function is studied in thermal quantum gravity, to one loop order. The leading (T ) contributions arising from internal gravitons are calculated and shown to be twice the ones associated with internal scalar particles, in correspondence with the two helicity states of the graviton. The gauge invariance of this result follows in consequence of ...

A Roman dominating function on a graph G is a function f : V (G) → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function is the value f(V (G)) = ∑ u∈V (G) f(u). The Roman domination number of G, γR(G), is the minimum weight of a Roman dominating function on G. In this paper, we...

The edge version of Szeged index and vertex version of PI index are defined very recently. They are similar to edge-PI and vertex-Szeged indices, respectively. The different versions of Szeged and PIindices are the most important topological indices defined in Chemistry. In this paper, we compute the edge-Szeged and vertex-PIindices of some important classes of benzenoid systems.

For any two vertices u and v in a connected graph G, a u − v path is a monophonic path if it contains no chords, and the monophonic distance dm(u, v) is the length of a longest u − v monophonic path in G. For any vertex v in G, the monophonic eccentricity of v is em(v) = max {dm(u, v) : u ∈ V}. The subgraph induced by the vertices of G having minimum monophonic eccentricity is the monophonic ce...

Consider the set SG(Qk) of all graphs whose vertices are labeled with non-identity elements of the group Qk = Z2 so that there is an edge between vertices with labels a and b if and only if the vertex labeled a + b is also in the graph. Note that edges always appear in triangles, since a + b = c, b + c = a and a + c = b are equivalent statements for Qk. We define the random cubic sum graph SG(Q...