Abstract In this paper we investigate certain fusion relations associated to an integrable vertex model on the square lattice which is invariant under Sp (4) symmetry. We establish a set of functional include transfer matrix inversion identity. The solution these in thermodynamic limit allows us compute partition function per site fundamental representation model. As byproduct also obtain mixin...

let g_1 and g_2 be simple connected graphs with disjoint vertex sets v(g_1) and v(g_2), respectively. for given vertices a_1in v(g_1) and a_2in v(g_2), a splice of g_1 and g_2 by vertices a_1 and a_2 is defined by identifying the vertices a_1 and a_2 in the :union: of g_1 and g_2. in this paper, we present exact formulas for computing some vertex-degree-based graph invariants of splice of graphs.

The vertex version of PI index is a molecular structure descriptor which is similar to vertex version of Szeged index. In this paper, we compute the vertex-PI index of TUC4C8(S), TUC4C8(R) and HAC5C7[r, p].

We investigate the influence of the full vacuum polarization and vertex function on the fermion propagator, using the coupled Dyson–Schwinger equations for the photon and fermion propagator. We show that, within a range of vertex functions, the general behavior of the fermion propagator does not depend on the exact details of the vertex, both in the massless and in the massive phase. Independen...

Label Representations • Let l ∈ Rd be the representation of label l, and f be a differentiable embedding function • For labels of label type i, we apply a learnable embedding function l = fi(l) • hi(v) is the embedding of label type i for vertex v: hi(v) = gi ({l | l ∈ labels of type i associated with vertex v}) • h̃i(v) is the reconstruction of the embedding of label type i for vertex v: h̃i(v) ...

A function f : V (G) → {0, 1, 2} is a Roman dominating function for a graph G = (V,E) if for every vertex v with f(v) = 0, there exists a vertex w ∈ N(v) with f(w) = 2. Emperor Constantine had the requirement that an army or legion could be sent from its home to defend a neighboring location only if there was a second army which would stay and protect the home. Thus, there are two types of armi...

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)) =

Let is a simple and connected graph with as vertex set edge set. Vertex labeling on inclusive local irregularity coloring defined by mapping the function of . In other words, an so that its weight value obtained adding up labels neighboring label. The chromatic number minimum colors from in G, denoted this paper, we learn about determine book graphs.