OMS-Vol. 2 (2018), Issue 1, pp. 371–378 Open Access Full-Text PDF

Abstract:A simple graph \(G=(V(G),E(G))\) admits an \(H\)-covering if \(\forall \ e \in E(G)\ \Rightarrow\ e \in E(H’)\) for some \((H’ \cong H )\subseteq G\). A graph \(G\) with \(H\) covering is an \((a,d)\)-\(H\)-antimagic if for bijection \(f:V\cup E \to \{1,2,\dots, |V(G)|+|E(G)| \}\), the sum of labels of all the edges and vertices belong to \(H’\) constitute an arithmetic progression \(\{a, a+d, \dots, a+(t-1)d\}\), where \(t\) is the number of subgraphs \(H’\). For \(f(V)= \{ 1,2,3,\dots,|V(G)|\}\), the graph \(G\) is said to be super \((a,d)\)-\(H\)-antimagic and for \(d=0\) it is called  \(H\)-supermagic. In this paper, we investigate the existence of super \((a,d)\)-\(C_3\)-antimagic labeling of a corona graph, for differences \(d=0,1,\dots, 5\).

OMS-Vol. 2 (2018), Issue 1, pp. 361–370 Open Access Full-Text PDF

Abstract:In this paper, we use the Delta Riemann-Liouville fractional integrals to establish some new integral inequalities for the Chebyshev functional in the case of two synchronous functions on time scales. Our results improve the inequalities for the discrete and continuous cases.