The complexity of highly interconnected systems is rooted in the interwoven architecture defined by its connectivity structure. In this paper, we develop matrix energy of the underlying connectivity structure as a measure of topological complexity and highlight interpretations abou...

A subset W of the vertices of a graph G is a resolving set for G when for each pair of distinct vertices u,v in V (G) there exists w in W such that d(u,w)≠d(v,w). The cardinality of a minimum resolving set for G is the metric dimension of G. This concept has applications in many diverse areas including network discovery, robot navigation, image processing, combinatorial search and optimization....

in this paper, we study projective randers change and c-conformal change of p-reduciblemetrics. then we show that every p-reducible generalized landsberg metric of dimension n  2 must be alandsberg metric. this implies that on randers manifolds the notions of generalized landsberg metric andberwald metric are equivalent.

Given a connected graph G, the metric (resp. edge metric) dimension of G is cardinality smallest ordered set vertices that uniquely identifies every pair distinct edges) by means distance vectors to such set. In this work, we settle three open problems on (edge) graphs. Specifically, show for r,t?2 with r?t, there n0, n?n0 exists order n r and t, which among other consequences, shows existence ...

We survey and present new geometric and combinatorial properties of some polyhedra with application in combinatorial optimization, for example, the max-cut and multicommodity ow problems. Namely we consider the volume, symmetry group, facets, vertices, face lattice, diameter, adjacency and incidence relations and connectivity of the metric polytope and its relatives. In particular, using its la...

Abst rac t . We survey and present new geometric and combinatorial propertiez of some polyhedra with application in combinatorial optimization, for example, the max-cut and multicommodity flow problems. Namely we consider the volume, symmetry group, facets, vertices, face lattice, diameter, adjacency and incidence relm :ons and connectivity of the metric polytope and its relatives. In partic~da...