The ball hypergraph of a graph G is the family balls all possible centers and radii in G. Balls subfamily are k-wise intersecting if intersection any k always nonempty. Helly number least integer greater than one such that every has nonempty common intersection. A k-Helly (or Helly, k=2) its at most k. We prove central vertex medians an n-vertex m-edge can be computed w.h.p. O˜(mn) time. Both r...

In this paper, we discuss the existence and uniqueness of points of coincidence and common fixed points for a pair of self-mappings satisfying some generalized contractive type conditions in $b$-metric spaces endowed with graphs and altering distance functions. Finally, some examples are provided to justify the validity of our results.

Let G be a graph and let S = (s1,s2,..., sk) non-decreasing sequence of positive integers. An S-packing coloring is mapping c : V(G) ? {1, 2,..., k} with the following property: if c(u) c(v) i, then d(u,v) > si for any i 2,...,k}. In particular, (1, 2, 3, ..., k), well known under name packing coloring. Next, r integer u,v V(G). A vertex u r-distance dominates v dG(u, v)? r. this paper, we p...