K-Banhatti Sombor Invariants of Certain Computer Networks

Topological Analysis and Synthesis of Structures related to Certain Classes of K-Geodetic Computer Networks

A fundamental characteristic of computer networks is their topological structure. The question of the description of the structural characteristics of computer networks represents a problem that is not completely solved. Search methods for structures of computer networks, for which the values of the selected parameters of their operation quality are extreme, have not been completely developed. ...

On finiteness of certain Vassiliev invariants

The best known examples of Vassiliev invariants are the coefficients of a Jones-type polynomial expanded after exponential substitution. We show that for a given knot, the first N Vassiliev invariants in this family determine the rest for some integer N . Supported in part by NSF Grant No. DMS-9504471 Supported in part by NSF Grant #23068 2 Kauffman, L. H. et. al. In this paper we prove a finit...

Group Invariants of Certain Burn Loop Classes

To any loop (L, ·), one can associate several groups, for example its multiplication groups Gleft(L) and Gright(L) and M(L) = 〈Gleft(L), Gright(L)〉, the groups of (left or right) pseudo-automorphisms, group of automorphisms, or the group of collineations of the associated 3-net. Groups, which are isotope invariants are of special interest. For example, the groups Gleft(L), Gright(L) and M(L) ar...

The K-Observer Problem in Computer Networks

For any non-negative integer K, aK-observer P of a network N is a set of nodes in N such that each message, that travels at least K hops in N , is handled (and so observed) by at least one node in P . A K-observer P of a network N is minimum iff the number of nodes in P is less than or equal the number of nodes in every K-observer of N . The nodes in a minimum K-observer of a network N can be u...

K F-invariants in Irreducible