Albertson M. O. Albertson, The irregularity of a graph, Ars Comb. 46 (1997) 219-225 je definiral irregularnost enostavnega neusmerjenega grafa ?$G$? kot ?$\text{irr}(G) = \sum_{uv \in E(G)} |d_G(u) - d_G(v)|$?, kjer ?$d_G(u)$? pomeni stopnjo vozlišča ?$u \in V(G)$?. Nedavno je bila v H. Abdo, S. Brandt and D. Dimitrov, The total irregularity of a graph, Discrete Math. Theor. Comput. Sci. 16 (2014), 201-206 definirana nova mera iregularnosti grafa, t.i. totalna iregularnost, in sicer kot ?$\text{irr}_t(G) = \frac{1}{2}\sum_{uv \in E(G)} |d_G(u) - d_G(v)|$?. Tukaj primerjamo iregularnost in totalno iregularnost grafov. Za povezan graf ?$G$? z ?$n$? vozlišči pokažemo, da je ?$\text{irr}_t(G) \le n^2 \text{irr}(G)/4$?. Še več, če je ?$G$? drevo, potem je ?$\text{irr}_t(G) \le (n-2) \text{irr}(G)$?.

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URN:NBN:SI:doc-O0OMKZI8

COBISSID

17578073

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29.05.2020

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APA:

Dimitrov, Darko, Škrekovski, Riste (2015). Comparing the irregularity and the total irregularity of graphs. Ars mathematica contemporanea, volume 9, issue 1, str. 45-50. URN:NBN:SI:doc-O0OMKZI8 from http://www.dlib.si

MLA:

Dimitrov, Darko, Škrekovski, Riste. "Comparing the irregularity and the total irregularity of graphs." Ars mathematica contemporanea volume 9. issue 1 (2015) str. 45-50.
<http://www.dlib.si/?URN=URN:NBN:SI:doc-O0OMKZI8>

Ars mathematica contemporanea
2008-
(Assembly record)