2016/07/14 by Imran Javaid, I. Irshad, Javaid, I. +5
Computer Science · Mathematics · #05C50 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.1607.04071
openalex publication_date 2016/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The zero forcing number of a graph G, denoted by Z(G), is the minimum cardinality of a set S of black vertices (where vertices in V(G)∖ S are colored white) such that V(G) is turned black after finitely many applications of "the color change rule": a white vertex is turned black if it is the only white neighbor of a black vertex. In this paper, we study the zero forcing number of corona product, G\odot H and lexicographic product, G∘ H of two graphs G and H. It is shown that if G and H are connected graphs of order n1≥2 and n2≥2 respectively, then Z(G\odot kH)=Z(G\odot k-1H)+n1(n2+1)k-1Z(H), where G\odotkH=(G\odotk-1H)\odot H. Also, it is shown that for a connected graph G of order n≥ 2 and an arbitrary graph H containing l≥ 1 components H1,H2, ⋯,Hl with |V(Hi)|=mi≥ 2, 1≤ i≤ l, (n-1)l+∑i=1l mi≤ Z(G∘ H)≤ n(∑i=1lmi)-l.