388 KB60 KB114 KB5 KB200820262026Lochan Patra, KamalPandey, Dineshletnik:26številka:3, article p3.02str. 1-24DOI:10.26493/1855-3974.3365.d2cISSN:1855-3974COBISSID_HOST:289610243URN:URN:NBN:SI:doc-58YWEL0RenUniverza na PrimorskemArs mathematica contemporaneacentercharacteristic centerconvex and concave functionscore centerjedro centrajedro podgrafakarakteristični centerkonveksne in konkavne funkcijemedianmedianasecurity centersubgraph corevarnostni centerCentrality in connected graphs via convexity or concavity|In graph theory, several central parts of graphs have been defined. The center, median and the security center are three such concepts defined for any connected graph, while others are specific to trees. These definitions typically involve a function defined on the vertex set of the graph. This paper generalizes the concepts of convex and concave functions, originally defined for trees, to connected graphs. Using this, we provide a unified approach to prove the known results that each of the center, median, and security center of a connected graph is either a cut vertex or lies within a block. Additionally, we introduce three new central parts of a connected graph as generalizations of the subtree core, core vertices, and characteristic set of a tree, and examine their properties in relation to the center, median, and security center. We also show that for any graph G, there exists a supergraph G' such that the subgraph induced by the characteristic center of G' is isomorphic to G. Finally, we propose several open problems related to subgraph core and core centerV teoriji grafov je bilo definiranih več centralnih delov grafov. Center, mediana in varnostni center so trije takšni pojmi, definirani za vsak povezan graf, medtem ko so nekateri drugi specifični za drevesa. Te definicije običajno temeljijo na funkciji, definirani na množici vozlišč grafa. V tem članku posplošimo pojma konveksne in konkavne funkcije, ki sta bila prvotno definirana za drevesa, na povezane grafe. Na tej osnovi podamo enoten pristop za dokazovanje znanih rezultatov, da je vsak izmed centra, mediane in varnostnega centra povezanega grafa bodisi ločitveno vozlišče bodisi leži znotraj bloka. Poleg tega uvedemo tri nove centralne dele povezanega grafa kot posplošitve jedra poddrevesa, jedrnih vozlišč in karakteristične množice drevesa ter preučimo njihove lastnosti v povezavi s centrom, mediano in varnostnim centrom. Pokažemo tudi, da za vsak graf G obstaja nadgraf G', tako da je podgraf, induciran s karakterističnim centrom grafa G', izomorfen grafu G. Nazadnje predlagamo več odprtih problemov, povezanih z jedrom podgrafa in jedrom centraTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije