The adjacent vertex-distinguishing proper edge-coloring is the minimum number of colors required for a G, in which no two vertices are incident to edges colored with same set colors. an G called edge-chromatic index. In this paper, I compute index Anti-prism, sunflower graph, double triangular winged prism, rectangular prism and Polygonal snake graph.

We introduce and investigate bucolic complexes, a common generalization of systolic complexes and of CAT(0) cubical complexes. They are defined as simply connected prism complexes satisfying some local combinatorial conditions. We study various approaches to bucolic complexes: from graph-theoretic and topological perspective, as well as from the point of view of geometric group theory. In parti...

We review a logic-based modeling language PRISM and report recent developments including belief propagation by the generalized inside-outside algorithm and generative modeling with constraints. The former implies PRISM subsumes belief propagation at the algorithmic level. We also compare the performance of PRISM with state-of-theart systems in statistical natural language processing and probabi...

We determine rank numbers for the prism graph P 2 ×C n (P 2 being the connected two-node graph and C n a cycle of length n) and for the square of an even cycle.

In this paper, we introduce and study a generalized Yosida approximation operator associated to H(·, ·)-co-accretive operator and discuss some of its properties. Using the concept of graph convergence and resolvent operator, we establish the convergence for generalized Yosida approximation operator. Also, we show an equivalence between graph convergence for H(·, ·)-co-accretive operator and gen...

Let G1 and G2 be disjoint copies of a graph G, and let f : V (G1) → V (G2) be a function. Then a functigraph C(G, f) = (V,E) has the vertex set V = V (G1) ∪ V (G2) and the edge set E = E(G1) ∪ E(G2) ∪ {uv | u ∈ V (G1), v ∈ V (G2), v = f(u)}. A functigraph is a generalization of a permutation graph (also known as a generalized prism) in the sense of Chartrand and Harary. In this paper, we study ...

Spectral graph theory discusses about the algebraic properties of graphs based on spectrum a graph. This article investigated prism The method used in this research is circulant matrix. results showed that P2,s regular degree 3, for s odd and ≥ circulantt with spectrum.

The probability that an embedding of a graph in Z 3 is knotted is investigated. For any given graph (embeddable in Z 3) without cut edges, it is shown that this probability approaches 1 at an exponential rate as the number of edges in the embedding goes to innnity. Furthermore, at least for a subset of these graphs, the rate at which the probability approaches 1 does not depend on the particula...

The prism over a graph G is the Cartesian product of with complete K2. A hamiltonian if there exists spanning cycle in G, and prism-hamiltonian hamiltonian. Rosenfeld Barnette (1973) [15] conjectured that every 3-connected planar prism-hamiltonian. We construct counterexample to conjecture.