Minimal sum labeling of graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10386748" target="_blank" >RIV/00216208:11320/18:10386748 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jda.2018.11.003" target="_blank" >https://doi.org/10.1016/j.jda.2018.11.003</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jda.2018.11.003" target="_blank" >10.1016/j.jda.2018.11.003</a>

Result language
angličtina
Original language name
Minimal sum labeling of graphs
Original language description
A graph G is called a sum graph if there is a so-called sum labeling of G, i.e. an injective function l : V(G) -> N such that for every u, v is an element of V (G) it holds that uv is an element of E(G) if and only if there exists a vertex w is an element of V (G) such that l(u) + l(v) = l(w). We say that sum labeling l is minimal if there is a vertex u is an element of V (G) such that l(u) = 1. In this paper, we show that if we relax the conditions (either allow non-injective labelings or consider graphs with loops) then there are sum graphs without a minimal labeling, which partially answers the question posed by Miller, Ryan and Smyth.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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