Distance magic graphs of high regularity

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F12%3A86084375" target="_blank" >RIV/61989100:27240/12:86084375 - isvavai.cz</a>
Alternative codes found
RIV/61989100:27740/12:86084375
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Distance magic graphs of high regularity
Original language description
A distance magic labeling of a graph G with n vertices is such a bijection f from the vertex set of G to the set of integers {1,2, ..., n } that for every vertex in G the sum of labels of all adjacent vertices gives the same value k. A graph that allowssuch a labeling is a distance magic graph. There is an elegant construction of r-regular distance magic graphs with an even number of vertices for all feasible values of r. For graphs of odd order certain necessary and certain sufficient conditions are known for the existence of a distance magic labeling. In this paper we show that an (n-3)-regular distance magic graph with n vertices exists iff n=3 (mod 6) and that its structure is determined uniquely. Moreover, we simplify the constructions from a recent paper by Fronček into a single construction and provide so another sufficient condition for the existence a distance magic graph with an odd number of vertices.
Czech name
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Czech description
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Project
<a href="/en/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: IT4Innovations Centre of Excellence</a>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP) Z - Vyzkumny zamer (s odkazem do CEZ) S - Specificky vyzkum na vysokych skolach

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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