Wszystkie pola: Vijayakumar, S. - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Clique irreducibility of some iterative classes of graphs
Autorzy:: Aparna Lakshmanan, S.
Vijayakumar, A.
Powiązania:: https://bibliotekanauki.pl/articles/743328.pdf
Data publikacji:: 2008
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: line graphs
Gallai graphs
anti-Gallai graphs
clique irreducible graphs
clique vertex irreducible graphs
Opis:: In this paper, two notions, the clique irreducibility and clique vertex irreducibility are discussed. A graph G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and it is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G. It is proved that L(G) is clique irreducible if and only if every triangle in G has a vertex of degree two. The conditions for the iterations of line graph, the Gallai graphs, the anti-Gallai graphs and its iterations to be clique irreducible and clique vertex irreducible are also obtained.
Źródło:: Discussiones Mathematicae Graph Theory; 2008, 28, 2; 307-321
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: On the uniqueness of $D$-vertex magic constant
Autorzy:: Arumugam, S.
Kamatchi, N.
Vijayakumar, G.R.
Powiązania:: https://bibliotekanauki.pl/articles/30148233.pdf
Data publikacji:: 2014-05-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: distance magic graph
D-vertex magic graph
magic constant
dominating function
fractional domination number
Opis:: Let $G = (V,E)$ be a graph of order n and let $D ⊆ {0, 1, 2, 3, . . .}$. For $v ∈ V$, let $N_D(v) = {u ∈ V : d(u, v) ∈ D}$. The graph $G$ is said to be $D$-vertex magic if there exists a bijection $f : V (G) → {1, 2, . . ., n}$ such that for all $v ∈ V, _{∑uv∈ND(v)} f(u)$ is a constant, called $D$-vertex magic constant. O’Neal and Slater have proved the uniqueness of the $D$-vertex magic constant by showing that it can be determined by the $D$-neighborhood fractional domination number of the graph. In this paper we give a simple and elegant proof of this result. Using this result, we investigate the existence of distance magic labelings of complete $r$-partite graphs where $r ≥ 4$.
Źródło:: Discussiones Mathematicae Graph Theory; 2014, 34, 2; 279-286
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

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