Λεπτομέρειες βιβλιογραφικής εγγραφής
| Τίτλος: |
The generalized 4-connectivity of a family of regular graphs. |
| Συγγραφείς: |
Zhao, Shu-Li1 (AUTHOR) zhaoshuli0210@126.com, Zhang, Bao-Cheng1 (AUTHOR) |
| Πηγή: |
Discrete Applied Mathematics. Dec2026, Vol. 394, p115-126. 12p. |
| Θεματικοί όροι: |
*Regular graphs, *Star graphs (Graph theory), *Computer network reliability, *Fault tolerance (Engineering), *Spanning trees |
| Περίληψη: |
Let G be a connected graph and S ⊆ V (G) with | S | ≥ 2. A tree T in G is called an S -tree if S ⊆ V (T). Two S -trees T 1 and T 2 are called internally disjoint if E (T 1) ∩ E (T 2) = 0̸ and V (T 1) ∩ V (T 2) = S. For an integer k with 2 ≤ k ≤ n , the generalized k -connectivity of a graph G is defined as κ k (G) = min { κ G (S) | S ⊆ V (G) and | S | = k } , where κ G (S) denotes the maximum number of internally disjoint S -trees in G. The generalized k -connectivity extends traditional connectivity and serves as a crucial measure for evaluating the reliability and fault tolerance of connecting any k vertices in G. In this paper, we mainly investigate the generalized 4-connectivity of a family of regular graph G n , which improves the known results about generalized 3-connectivity of G n in Zhao et al., (2021). For a reason that the alternating group network A N n , the star graph S n and pancake graphs P n are special cases of the regular graph G n , as applications of the main result, we obtain that κ 4 (A N n) = n − 2 for n ≥ 4 , κ 4 (S n) = n − 2 for n ≥ 3 and κ 4 (P n) = n − 2 for n ≥ 3. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: |
Academic Search Index |