In a graph G, a k-container Ck(u, v) is a set of k disjoint paths joining u and v. A k-container Ck(u, v) is k ∗-container if every vertex of G is passed by some path in Ck(u, v). A graph G is k ∗-connected if there exists a k∗-container between any two vertices. An m-regular graph G is super-connected if G is k∗-connected for any k with 1 k m. In this paper, we prove that the recursive circula...

A graph G of order p and size q is called (a, d)-edge-antimagic total if there exists a bijective function f : V (G) ∪ E(G) → {1, 2, . . . , p + q} such that the edge-weights w(uv) = f(u) + f(v) + f(uv), uv ∈ E(G), form an arithmetic sequence with first term a and common difference d. The graph G is said to be super (a, d)-edge-antimagic total if the vertex labels are 1, 2, . . . , p. In this p...

An even 2-factor is one such that each cycle of length. A 4- regular graph G 4-edge-colorable if and only has two edge-disjoint 2- factors whose union contains all edges in G. It known the line a cubic without 3-edge-coloring not 4-edge-colorable. Hence, we are interested whether those graphs have an 2-factor. Bonisoli Bonvicini proved connected with number 2-factor, perfect matching [Even cycl...

Variation in tone fundamental frequency in Mandarin has long attracted intensive research focusing on the underlying factors that affect tonal shape. The current paper focuses on tone f0 shape different modes of speech and presents our results delineating the diversity of tonal f0 contour and how contextual elements affect realized tone shape in an acoustic environment with high variance of ton...