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Convex Sets Under Some Graph Operations
We characterize convex sets of graphs resulting from some binary operations, and compute the convexity numbers of the resulting graphs. Expand
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We present two convergence theorems for the H1-integral. The Henstock integral is now relatively well-known. An attempt has been made by Garces, Lee, and Zhao (2) to define the Henstock integral asExpand
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Ateneo de Manila University
Park, Ryu, and Lee recently defined a Henstock-type integral, which lies entirely between the McShane and the Henstock integrals. This paper presents two characterizing convergence conditions forExpand
Metric graphic sets
Revisiting a Number-Theoretic Puzzle: The Census-Taker Problem
The current work revisits the results of L.F. Meyers and R. See in [3], and presents the census-taker problem as a motivation to introduce the beautiful theory of numbers.
On completely k-magic regular graphs
Let k be a positive integer. A graph G = (V (G), E(G)) is said to be k-magic if there is a function (or edge labeling) ` : E(G)→ Zk \ {0}, where Z1 = Z, such that the induced function (or vertexExpand
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Computing the metric dimension of truncated wheels
For an ordered subset W = {w1, w2, w3, . . . , wk} of vertices in a connected graph G and a vertex v of G, the metric representation of v with respect to W is the k-vector r(v|W ) = (d(v, w1), d(v,Expand
The null set of the join of paths
For positive integer k, a graph G is said to be k-magic if the edges of G can be labeled with the nonzero elements of Abelian group ℤk, where ℤ1 = ℤ (the set of integers) and ℤk is the group of int...
Characterization of Completely $k$-Magic Regular Graphs
Let $k \in \mathbb{N}$ and $c \in \mathbb{Z}_k$, where $\mathbb{Z}_1=\mathbb{Z}$. A graph $G=(V(G),E(G))$ is said to be $c$-sum $k$-magic if there is a labeling $\ell:E(G) \rightarrow \mathbb{Z}_kExpand