A graph is called self–centered if all of its vertices have the same eccentricity. We prove some new properties of such graphs and obtain all minimal self–centered graphs of up to 10 vertices.

In this paper the idea of strong sum distance which is a metric, in a fuzzy graph is introduced. Based on this metric the concepts of eccentricity, radius, diameter, center and self centered fuzzy graphs are studied. Some properties of eccentric nodes, peripheral nodes and central nodes are obtained. A characterisation of self centered complete fuzzy graph is obtained and conditions under which...

Almost self-centered graphs were recently introduced as the graphs with exactly two non-central vertices. In this paper we characterize almost selfcentered graphs among median graphs and among chordal graphs. In the first case P4 and the graphs obtained from hypercubes by attaching to them a single leaf are the only such graphs. Among chordal graph the variety of almost self-centered graph is m...

For p∈N, a coloring λ of the vertices graph G is p-centered if for every connected subgraph H G, either receives more than p colors under or there color that appears exactly once in H. Centered colorings play an important role theory sparse classes introduced by Nešetřil and Ossona de Mendez [31], [32], as they structurally characterize bounded expansion — one key sparsity notions this theory. ...

Wesurvey results and open problems in hamiltonian graph theory centered around two conjectures of the 1980s that are still open: every 4-connected claw-free graph (line graph) is hamiltonian. These conjectures have lead to awealth of interesting concepts, techniques, results and equivalent conjectures.

Computational Linguistics (CL) associated with the Internet of Multimedia Things (IoMT)-enabled multimedia computing applications brings several research challenges, such as real-time speech understanding, deep fake video detection, emotion recognition, home automation, and so on. Due to emergence machine translation, CL solutions have increased tremendously for different natural language proce...

Our aim here is to address the problem of decomposing a whole network into a minimal number of ego–centered subnetworks. For this purpose, the network egos are picked out as the members of a minimum dominating set of the network. However, to find such an efficient dominating ego–centered construction, we need to be able to detect all the minimum dominating sets and to compare all the correspond...

Let T be a finite tree graph, TN be the Cartesian power graph of T , and dN be the graph distance metric on TN . Also let Sr (x) := {v ∈ T N : d (x, v) = r} be the sphere of radius r centered at x and M be the spherical maximal averaging operator on TN given by Mf(x) := sup r≥0 S N r (x) 6=∅ 1 |Sr (x)| ∣

because of its widespread needs in different scientific fields, statistics and probability theory have gained great importance and medical students as well as students of other medically related disciplines including nursing need to use them especially in their research projects in undergraduate, graduate and postgraduate schools. this article deals with the question of finding the most effecti...