- Tytuł:
- Nowhere-Zero Unoriented 6-Flows on Certain Triangular Graphs
- Autorzy:
-
Yang, Fan
Li, Liangchen
Zhou, Sizhong - Powiązania:
- https://bibliotekanauki.pl/articles/32309450.pdf
- Data publikacji:
- 2022-08-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
nowhere-zero k -flow
triangle-tree
triangle-star
bidirected graph - Opis:
- A nowhere-zero unoriented flow of graph G is an assignment of non-zero real numbers to the edges of G such that the sum of the values of all edges incident with each vertex is zero. Let k be a natural number. A nowhere-zero unoriented k-flow is a flow with values from the set {±1, . . ., ±(k − 1)}, for short we call it NZ-unoriented k-flow. Let H1 and H2 be two graphs, H1⊕H2 denote the 2-sum of H1 and H2, if E(H1⊕H2) = E(H1) ∪ E(H2), |V(H1)∩V(H2)|=2, and |E(H1)∩E(H2)| = 1. A triangle-path in a graph G is a sequence of distinct triangles T1, T2, . . ., Tm in G such that for 1 ≤ i ≤ m, |E(Ti)∩E(Ti+1)| = 1 and E(Ti)∩E(Tj)=∅ if j>i+1. A triangle-star is a graph with triangles such that each triangle having one common edges with other triangles. Let G be a graph which can be partitioned into some triangle-paths or wheels H1, H2, . . ., Ht such that G = H1⊕H2⊕...⊕Ht. In this paper, we prove that G except a triangle-star admits an NZ-unoriented 6-flow. Moreover, if each Hi is a triangle-path, then G except a triangle-star admits an NZ-unoriented 5-flow.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2022, 42, 3; 727-746
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł