Autor: MEL. - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Wiener index of generalized stars and their quadratic line graphs
Autorzy:: Dobrynin, Andrey
Mel'nikov, Leonid
Powiązania:: https://bibliotekanauki.pl/articles/743914.pdf
Data publikacji:: 2006
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: distance in a graph
Wiener index
star
iterated line graph
Opis:: The Wiener index, W, is the sum of distances between all pairs of vertices in a graph G. The quadratic line graph is defined as L(L(G)), where L(G) is the line graph of G. A generalized star S is a tree consisting of Δ ≥ 3 paths with the unique common endvertex. A relation between the Wiener index of S and of its quadratic graph is presented. It is shown that generalized stars having the property W(S) = W(L(L(S)) exist only for 4 ≤ Δ ≤ 6. Infinite families of generalized stars with this property are constructed.
Źródło:: Discussiones Mathematicae Graph Theory; 2006, 26, 1; 161-175
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: 4-chromatic Koester graphs
Autorzy:: Dobrynin, Andrey
Mel'nikov, Leonid
Powiązania:: https://bibliotekanauki.pl/articles/743274.pdf
Data publikacji:: 2012
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: planar graph
4-critical graph
Grötzsch-Sachs graph
Koester graph
Opis:: Let G be a simple 4-regular plane graph and let S be a decomposition of G into edge-disjoint cycles. Suppose that every two adjacent edges on a face belong to different cycles of S. Such a graph G arises as a superposition of simple closed curves in the plane with tangencies disallowed. Studies of coloring of graphs of this kind were originated by Grötzsch. Two 4-chromatic graphs generated by circles in the plane were constructed by Koester in 1984 [10,11,12]. Until now, no other examples of such graphs were known. We present fourteen new 4-chromatic graphs generated by circles in the plane.
Źródło:: Discussiones Mathematicae Graph Theory; 2012, 32, 4; 617-627
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Erdős regular graphs of even degree
Autorzy:: Dobrynin, Andrey
Mel'nikov, Leonid
Pyatkin, Artem
Powiązania:: https://bibliotekanauki.pl/articles/743782.pdf
Data publikacji:: 2007
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: vertex coloring
4-critical graph
circulant
regular graph
vertex connectivity
Opis:: In 1960, Dirac put forward the conjecture that r-connected 4-critical graphs exist for every r ≥ 3. In 1989, Erdös conjectured that for every r ≥ 3 there exist r-regular 4-critical graphs. A method for finding r-regular 4-critical graphs and the numbers of such graphs for r ≤ 10 have been reported in [6,7]. Results of a computer search for graphs of degree r = 12,14,16 are presented. All the graphs found are both r-regular and r-connected.
Źródło:: Discussiones Mathematicae Graph Theory; 2007, 27, 2; 269-279
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

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