We show that for every integer k ≥ 2 and every k graphs G1, G2, . . . , Gk, there exists a hull graph with k hull vertices v1, v2, . . . , vk such that link L(vi) = Gi for 1 ≤ i ≤ k. Moreover, every pair a, b of integers with 2 ≤ a ≤ b is realizable as the hull number and geodetic number (or upper geodetic number) of a hull graph. We also show that every pair a, b of integers with a ≥ 2 and b ≥...

In this paper, we show that the class of all properly 3-realizable groups is closed under amalgamated free products (and HNN-extensions) over finite groups. We recall that G is said to be properly 3-realizable if there exists a compact 2-polyhedron K with π1(K) = G and whose universal cover K̃ has the proper homotopy type of a 3-manifold (with boundary).

Several rigorous turbulent models have been developed in the past years and it can be seen that more research is needed to reach a better understanding of their generality and precision by verifying their applications for distinct hydraulic phenomena; under certain assumptions. This survey evaluates the performance of Standard k-ε, Realizable k-ε, RNG k-ε, k-ω and RSM models in predicting flow ...

In this study, the thermal characteristics of turbulent nanofluid flow in a helical tube in the tube heat exchanger (HTTHE) were assessed numerically through computational fluid dynamics (CFD) simulation. The findings of both the turbulent models: realizable k-epsion (k-ε) and re-normalisation group (RNG) k-epsilon were compared. The temperature distribution contours show that realizable and RN...

A companionship argument is used to give a constructive geometric proof of a key result concerning the knot homomorph problem: Given elements p and A in a group G, is there a knot K in S3 and a surjective representation p : n,(S3 K) + G, such that p(m) = y and p( [) = A, where m and I are the meridian and longitude of K. The result presented here is that if for some p that normally generates G,...

We study, in three parts, degree sequences of k-families (or k-uniform hypergraphs) and shifted k-families. • The first part collects for the first time in one place, various implications such as Threshold ⇒ Uniquely Realizable ⇒ Degree-Maximal ⇒ Shifted which are equivalent concepts for 2-families (= simple graphs), but strict implications for kfamilies with k ≥ 3. The implication that uniquel...

The packing chromatic number χρ(G) of a graphG is the smallest integer k such that the vertex set of G can be partitioned into sets Vi, i ∈ [k], where each Vi is an i-packing. In this paper, we investigate for a given triple (a, b, c) of positive integers whether there exists a graph G such that ω(G) = a, χ(G) = b, and χρ(G) = c. If so, we say that (a, b, c) is realizable. It is proved that b =...

The niche graph of a digraph $D$ has $V(D)$ as the vertex set and an edge $uv$ if only $(u,w) \in A(D)$ $(v,w) A(D)$, or $(w,u) $(w,v) for some $w V(D)$. notion was introduced by Cable et al. (1989) variant competition graph. If is $D$, it said to be niche-realizable through $D$. $G$ $k$-partite tournament integer $k \ge 2$, then we say that pair $(G, k)$ niche-realizable. Bowser (1999) studied...