A Discrete Intermediate Value Theorem

Zumkeller Labeling Algorithms for Complete Bipartite Graphs and Wheel Graphs

“…In this section, we introduce new labeling of graphs using Zumkeller numbers and prove that complete bipartite graphs [8] and wheel-related graphs admit Zumkeller labeling.…”

“…In this paper, we provide algorithms to obtain Zumkeller labeling for complete bipartite graph [8] and wheel graphs. We refer a programming language slightly adapted to C, given by Frank Buss [9] to identify the Zumkeller numbers and Zumkeller partitions.…”

Best Proximity Point Results in Non-Archimedean Modular Metric Space

“…We identify G with the pair (V(G), E(G)). Furthermore, we may handle G as a weighted graph (see [23], p. 309) by assigning to every edge the distance between its vertices. If x and y are vertices in a graph G, then a path in G from x to y of length N (N ∈ N) is a sequence {x i } N i=0 of N + 1 vertices, such that x 0 = x, x N = y and (x i−1 , x i ) ∈ E(G) for i = 1, .…”

Fibonacci Powers and a Fascinating Triangle

“…Our first method involves writing the Fibonacci sequence in terms of its explicit formula for n > 0, where a = (1 +V5)/2 and (3 = (1 ?\/5)/2 [5], [6]. Less well known is that there is a recurrence relation for F2, which can be found in at least two different ways.…”