Jia Jie Liu

The Hub Number of Sierpiński-Like Graphs

A set Q⊆V is a hub set of a graph G=(V,E) if, for every pair of vertices u,v∈V∖Q, there exists a path from u to v such that all intermediate vertices are in Q. The hub number of G is the minimum size of a hub set in G. This paper derives the hub numbers of Sierpiński-like graphs including: Sierpiński graphs, extended Sierpiński graphs, and Sierpiński gasket graphs. Meanwhile, the corresponding minimum hub sets are also obtained.

Global Strong Defensive Alliances of Sierpiński-Like Graphs

A strong alliance in a graph G=(V,E) is a set of vertices S⊆V satisfying the condition that, for each v∈S, the number of its neighbors, including itself, in S is greater than the number of those neighbors not in S. A strong alliance S is global if S forms a dominating set of G. In this paper, we shall propose a way for finding a minimum global strong alliance for each of those Sierpiński-like graphs. Furthermore, we also derive the exact values of those global strong alliance numbers.

The Outer-connected Domination Number of Sierpiński-like Graphs

An outer-connected dominating set in a graph G = (V, E) is a set of vertices D ⊆ V satisfying the condition that, for each vertex v ∉ D, vertex v is adjacent to some vertex in D and the subgraph induced by V∖D is connected. The outer-connected dominating set problem is to find an outer-connected dominating set with the minimum number of vertices which is denoted by γ~c(G)

Constrained Longest Common Subsequences with Run-Length-Encoded Strings

\tilde {\gamma }_{c}(G)

The 2-Rainbow Domination of Sierpiński Graphs and Extended Sierpiński Graphs

. In this paper, we determine γ~c(S(n,k))

The connected p -median problem on block graphs

\tilde {\gamma }_{c}(S(n,k))

The hub number of co-comparability graphs

, γ~c(S+(n,k))

An Optimal Algorithm for Untangling Binary Trees via Rotations

\tilde {\gamma }_{c}(S^{+}(n,k))

An Optimal Rotation Distance Set

, γ~c(S++(n,k))

A fast algorithm for finding the positions of all squares in a run-length encoded string

\tilde {\gamma }_{c}(S^{++}(n,k))