In 1980, Enomoto et al. proposed the conjecture that every tree is a super (a, 0)-edge-antimagic total graph. In this paper, we give a partial support for the correctness of this conjecture by formulating some super (a, d)edge-antimagic total labelings on a subclass of subdivided stars denoted by T (n, n + 1, 2n + 1, 4n + 2, n5, n6, . . . , nr) for different values of the edgeantimagic labeling...

Not long ago, Bagga, Beineke, and Varma [1] defined the super line multigraph of a simple graph Γ = (V,E) to be the graph Mr(Γ) whose vertex set is Pr(E), the class of r-element subsets of the edge set, and with an adjacency R ∼ R′ (where R,R′ ∈ Pr(E)) for every edge pair (e, f) with e ∈ R and f ∈ R′ such that e and f are adjacent in Γ. Thus, the number of edges joining R and R′ in Mr(Γ) is the...

An (a, d)-edge-antimagic total labeling of G is a one-to-one mapping g taking the vertices and edges onto 1, 2, . . . , |V (G)| + |E(G)| so that the edgeweights w(uv) = g(u) + g(v) + g(uv), uv ∈ E(G), form an arithmetic progression with initial term a and common difference d. Such a labeling is called super if the smallest labels appear on the vertices. In this paper, we investigate the existen...

As applications involving the capture of digital images and video become more demanding in the recent years and at the same time more ambitious for critical real time applications like video surveillance. There is a driving need for digital images and videos of higher resolutions and visual quality. Since, the video is a sequence of still images representing scenes in motion, the problem of gen...

In this study, turning operation of Monel K500 copper-nickel super-alloy was evaluated. Ceramic cutting tools with two different cutting noses (conventional and wiper) were utilized. At first, the experimental tests were designed by using central composite design method. After implementation of the tests, the statistical models for output data (surface roughness, cutting force, and flank wear) ...

Let G be a (p, q) graph and let f : V (G) → {1, 2, 3, · · · , p + q} be an injection. For each edge e = uv, let f∗(e) = (f(u)+f(v))/2 if f(u)+f(v) is even and f∗(e) = (f(u)+f(v)+1)/2 if f(u) + f(v) is odd. Then f is called a super mean labeling if f(V ) ∪ {f∗(e) : e ∈ E(G)} = {1, 2, 3, · · · , p+ q}. A graph that admits a super mean labeling is called a super mean graph. In this paper we presen...

Here, we give a full proof of Theorem 1. Recall that an equivalent construction of the PAGA graphs is obtained by collapsing the graph G 1 to G t m leading to t super nodes. Accordingly, based on G t m, we can directly generate G m by (temporarily) adding m more nodes, each linking with a single edge, and then collapsing these m nodes to the (t+ 1)th super node. Let dt,i(v) denote the degree of...