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master's thesis
Frog jumping problem on simple graphs
2022. urn:nbn:hr:126:766253
Veselovac, Matej
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

Cite this document

Veselovac, M. (2022). Frog jumping problem on simple graphs (Master's thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:766253

Veselovac, Matej. "Frog jumping problem on simple graphs." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:766253

Veselovac, Matej. "Frog jumping problem on simple graphs." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2022. https://urn.nsk.hr/urn:nbn:hr:126:766253

Veselovac, M. (2022). 'Frog jumping problem on simple graphs', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 28 March 2023, https://urn.nsk.hr/urn:nbn:hr:126:766253

Veselovac M. Frog jumping problem on simple graphs [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2022 [cited 2023 March 28] Available at: https://urn.nsk.hr/urn:nbn:hr:126:766253

M. Veselovac, "Frog jumping problem on simple graphs", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2022. Available at: https://urn.nsk.hr/urn:nbn:hr:126:766253

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Metadata
TitleFrog jumping problem on simple graphs
Title (croatian)Problem skakanja žaba na jednostavnim grafovima
AuthorMatej Veselovac
MentorSnježana Majstorović (mentor)
Committee memberKristian Sabo (predsjednik povjerenstva)
Committee memberDomagoj Matijević (član povjerenstva)
Committee memberMirela Jukić Bokun (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2022-10-21, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Discrete and Combinatorial Mathematics
Abstract
Frog jumping problem is played on a simple connected graph. Initially, one frog is placed on each vertex of a graph and the goal is to move all frogs to a single vertex. If there are m frogs on a vertex u, then it is allowed to move them on a vertex v if and only if u and v are connected by a shortest path consisted of m edges. We solve the problem for path graphs, star graphs, starfish graphs, and a subset of dandelion graphs. We conjecture that all vertices of a sufficiently large complete binary tree are solvable. The problem is a generalization of the “Frog jumping” problem by G. Hamilton
Abstract (croatian)
Problem skakanja žaba se postavlja na jednostavnom povezanom grafu. Na početku se postavlja jedna žaba na svaki vrh, s ciljem da se sve žabe u konačnici sretnu u istom vrhu. Pomicanje svih x žaba s jednog vrha na drugi je dozvoljeno ako i samo ako su izabrani vrhovi neprazni i povezani putem koji se sastoji od x različitih bridova. Rješavamo problem na putevima, zvijezdama, zvjezdača grafovima, te na podskupu maslačak grafova. Nagađamo da su svi vrhovi na svim dovoljno velikim potpunim binarnim stablima rješivi. Ovaj problem je generalizacija problema “Frog jumping” od G. Hamilton.
Keywords
Keywords (croatian)
Languageenglish
URN:NBNurn:nbn:hr:126:766253
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2022-10-24 12:01:18