20.500.12556/RUP-23503 Centrality in connected graphs via convexity or concavity Centralnost v povezanih grafih z vidika konveksnosti ali konkavnosti 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 center. V 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 centra. Center characteristic center convex and concave functions core center median security center subgraph core Center karakteristični center konveksne in konkavne funkcije jedro centra mediana varnostni center jedro podgrafa true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2026-08-17 10:58:30 2026-08-17 10:58:30 2026-08-18 03:07:46 0000-00-00 00:00:00 2026 0 0 24 str. no. 3, [article no.] P3.02 Vol. 26 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-05-26 51 1855-3974 10.26493/1855-3974.3365.d2c AMC_Pandey,_Lochan_Patra_2026.pdf AMC_Pandey,_Lochan_Patra_2026.pdf 1 AE2114DC3D5C8BDC2EE9A402675B2016 72d466611f8c5c40af6b8d0c35f08cc09c7977b633b8d74c824ab460db9e03fa a51c86ac-9a1a-11f1-9e8d-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=34495 Založba Univerze na Primorskem 0 0 0