Totally antimagic total graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F15%3A43924760" target="_blank" >RIV/49777513:23520/15:43924760 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Totally antimagic total graphs
Original language description
For a graph G, a bijection from the vertex set and the edge set of G to the set {1,2,...,|V(G)|+|E(G)|} is called a total labeling of G. The edge-weight of an edge is the sum of the label of the edge and the labels of the end vertices of that edge. The vertex-weight of a vertex is the sum of the label of the vertex and the labels of all the edges incident with that vertex. A total labeling is called edge-antimagic total (vertex antimagic total) if all edge-weights (vertex-weights) are pairwise distinct.If a labeling is simultaneously edge-antimagic total and vertex-antimagic total it is called a totally antimagic total labeling. A graph that admits totally antimagic total labeling is called a totally antimagic total graph. In this paper we deal with the problem of finding totally antimagic total labeling of some classes of graphs. We prove that paths, cycles, stars, double-stars and wheels are totally antimagic total. We also show that a union of regular totally antimagic total graphs
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/ED1.1.00%2F02.0090" target="_blank" >ED1.1.00/02.0090: NTIS - New Technologies for Information Society</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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