Temat: regular graph - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: Tree domatic number in graphs
Autorzy:: Chen, X. G.
Tematy:: tree domatic number
regular graph
planar graph
Cartesian product; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/255594.pdf Link otwiera się w nowym oknie
Opis:: A dominating set S in a graph G is a tree dominating set of G if the subgraph induced by S is a tree. The tree domatic number of G is the maximum number of pairwise disjoint tree dominating sets in V(G). First, some exact values of and sharp bounds for the tree domatic number are given. Then, we establish a sharp lower bound for the number of edges in a connected graph of given order and given tree domatic number, and we characterize the extremal graphs. Finally, we show that a tree domatic number of a planar graph is at most 4 and give a characterization of planar graphs with the tree domatic number 3.
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: On Order Prime Divisor Graphs of Finite Groups
Autorzy:: Sen, Mridul K.
Maity, Sunil K.
Das, Sumanta
Tematy:: group
dihedral group
complete graph
Eulerian graph
regular graph
planar graph
order prime divisor graph; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/55795862.pdf Link otwiera się w nowym oknie
Opis:: The order prime divisor graph $\mathscr{PD}(G)$ of a finite group $G$ is a simple graph whose vertex set is $G$ and two vertices $a, b ∈ G$ are adjacent if and only if either $ab = e$ or $o(ab)$ is some prime number, where $e$ is the identity element of the group $G$ and $o(x)$ denotes the order of an element $x ∈ G$. In this paper, we establish the necessary and sufficient condition for the completeness of order prime divisor graph $\mathscr{PD}(G)$ of a group $G$. Concentrating on the graph $\mathscr{PD}(D_n)$, we investigate several properties like degrees, girth, regularity, Eulerianity, Hamiltonicity, planarity etc. We characterize some graph theoretic properties of $\mathscr{PD}(ℤ_n), \mathscr{PD}(S_n), \mathscr{PD}(A_n)$.
Dostawca treści:: Biblioteka Nauki

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