Matches in SemOpenAlex for { <https://semopenalex.org/work/W2014251935> ?p ?o ?g. }
Showing items 1 to 87 of
87
with 100 items per page.
- W2014251935 endingPage "780" @default.
- W2014251935 startingPage "771" @default.
- W2014251935 abstract "For two vertices u and v of a graph G, the closed interval I[u, v] consists of u, v, and all vertices lying in some u−v geodesic of G, while for S ⫅ V(G), the set I[S] is the union of all sets I[u, v] for u, v ε S. A set S of vertices of G for which I[S] = V(G) is a geodetic set for G, and the minimum cardinality of a geodetic set is the geodetic number g(G). A vertex v in G is an extreme vertex if the subgraph induced by its neighborhood is complete. The number of extreme vertices in G is its extreme order ex(G). A graph G is an extreme geodesic graph if g(G) = ex(G), that is, if every vertex lies on a u−v geodesic for some pair u, v of extreme vertices. It is shown that every pair a, b of integers with 0 ⩽ a ⩽ b is realizable as the extreme order and geodetic number, respectively, of some graph. For positive integers r, d, and k ⩾ 2, it is shown that there exists an extreme geodesic graph G of radius r, diameter d, and geodetic number k. Also, for integers n, d, and k with 2 ⩽ d > n, 2 ⩽ k > n, and n − d − k + 1 ⩾ 0, there exists a connected extreme geodesic graph G of order n, diameter d, and geodetic number k. We show that every graph of order n with geodetic number n − 1 is an extreme geodesic graph. On the other hand, for every pair k, n of integers with 2 ⩽ k ⩽ n − 2, there exists a connected graph of order n with geodetic number k that is not an extreme geodesic graph." @default.
- W2014251935 created "2016-06-24" @default.
- W2014251935 creator A5055151897 @default.
- W2014251935 creator A5076706719 @default.
- W2014251935 date "2002-12-01" @default.
- W2014251935 modified "2023-10-11" @default.
- W2014251935 title "Extreme Geodesic Graphs" @default.
- W2014251935 cites W110075881 @default.
- W2014251935 cites W1583458608 @default.
- W2014251935 cites W1963891388 @default.
- W2014251935 cites W1971489812 @default.
- W2014251935 cites W1989512718 @default.
- W2014251935 cites W2023812709 @default.
- W2014251935 cites W2032676828 @default.
- W2014251935 cites W2038715674 @default.
- W2014251935 cites W2044108353 @default.
- W2014251935 cites W2169204877 @default.
- W2014251935 cites W2724587737 @default.
- W2014251935 cites W2935684492 @default.
- W2014251935 cites W4213214460 @default.
- W2014251935 doi "https://doi.org/10.1023/b:cmaj.0000027232.97642.45" @default.
- W2014251935 hasPublicationYear "2002" @default.
- W2014251935 type Work @default.
- W2014251935 sameAs 2014251935 @default.
- W2014251935 citedByCount "24" @default.
- W2014251935 countsByYear W20142519352012 @default.
- W2014251935 countsByYear W20142519352013 @default.
- W2014251935 countsByYear W20142519352015 @default.
- W2014251935 countsByYear W20142519352016 @default.
- W2014251935 countsByYear W20142519352017 @default.
- W2014251935 countsByYear W20142519352018 @default.
- W2014251935 countsByYear W20142519352020 @default.
- W2014251935 countsByYear W20142519352021 @default.
- W2014251935 countsByYear W20142519352022 @default.
- W2014251935 countsByYear W20142519352023 @default.
- W2014251935 crossrefType "journal-article" @default.
- W2014251935 hasAuthorship W2014251935A5055151897 @default.
- W2014251935 hasAuthorship W2014251935A5076706719 @default.
- W2014251935 hasConcept C114614502 @default.
- W2014251935 hasConcept C118615104 @default.
- W2014251935 hasConcept C121134508 @default.
- W2014251935 hasConcept C132525143 @default.
- W2014251935 hasConcept C149530733 @default.
- W2014251935 hasConcept C165818556 @default.
- W2014251935 hasConcept C203776342 @default.
- W2014251935 hasConcept C205649164 @default.
- W2014251935 hasConcept C2524010 @default.
- W2014251935 hasConcept C33923547 @default.
- W2014251935 hasConcept C58640448 @default.
- W2014251935 hasConcept C58754882 @default.
- W2014251935 hasConcept C76444178 @default.
- W2014251935 hasConcept C80899671 @default.
- W2014251935 hasConceptScore W2014251935C114614502 @default.
- W2014251935 hasConceptScore W2014251935C118615104 @default.
- W2014251935 hasConceptScore W2014251935C121134508 @default.
- W2014251935 hasConceptScore W2014251935C132525143 @default.
- W2014251935 hasConceptScore W2014251935C149530733 @default.
- W2014251935 hasConceptScore W2014251935C165818556 @default.
- W2014251935 hasConceptScore W2014251935C203776342 @default.
- W2014251935 hasConceptScore W2014251935C205649164 @default.
- W2014251935 hasConceptScore W2014251935C2524010 @default.
- W2014251935 hasConceptScore W2014251935C33923547 @default.
- W2014251935 hasConceptScore W2014251935C58640448 @default.
- W2014251935 hasConceptScore W2014251935C58754882 @default.
- W2014251935 hasConceptScore W2014251935C76444178 @default.
- W2014251935 hasConceptScore W2014251935C80899671 @default.
- W2014251935 hasIssue "4" @default.
- W2014251935 hasLocation W20142519351 @default.
- W2014251935 hasOpenAccess W2014251935 @default.
- W2014251935 hasPrimaryLocation W20142519351 @default.
- W2014251935 hasRelatedWork W1671947312 @default.
- W2014251935 hasRelatedWork W1964058826 @default.
- W2014251935 hasRelatedWork W1964592620 @default.
- W2014251935 hasRelatedWork W2032676828 @default.
- W2014251935 hasRelatedWork W2348525925 @default.
- W2014251935 hasRelatedWork W2375781598 @default.
- W2014251935 hasRelatedWork W2394358482 @default.
- W2014251935 hasRelatedWork W2616356260 @default.
- W2014251935 hasRelatedWork W3092119098 @default.
- W2014251935 hasRelatedWork W32827807 @default.
- W2014251935 hasVolume "52" @default.
- W2014251935 isParatext "false" @default.
- W2014251935 isRetracted "false" @default.
- W2014251935 magId "2014251935" @default.
- W2014251935 workType "article" @default.