A New Approach in Finding Full Friendly Indices

作者：Gao, Zhen-Bin; Ren, Hong-Nan; Lee, Sin-Min; Han, Ruo-Yuan; Lau, Gee-Choon^*

来源：Bulletin of the Malaysian Mathematical Sciences Society, 2018, 41(1): 443-453.

DOI：10.1007/s40840-016-0373-8

• Vertex labeling
• Friendly labeling
• Full friendly index set
• Full vertices blow-up
• Embedding labeling graph method

Let G be a graph with vertex set V(G) and edge set E(G), a vertex labeling f : V(G) -> Z(2) induces an edge labeling f (+) : E(G) -> Z(2) defined by f (+)(xy) = f (x) + f (y), for each edge xy is an element of E(G). For each i is an element of Z(2), let v f (i) = vertical bar{u is an element of V(G) : f (u) = i}vertical bar and e(f) +(i) = |{xy is an element of E(G) : f (+)(xy) = i}vertical bar. A vertex labeling f of a graph G is said to be friendly if vertical bar v(f) (1) -v(f) (0)vertical bar <= 1. The friendly index set of the graph G, denoted by F I(G), is defined as {vertical bar e(f) +(1) -e(f) +(0)vertical bar : the vertex labeling f is friendly}. The full friendly index set of the graph G, denoted by FFI (G), is defined as {e(f) +(1) -e(f) +(0) : the vertex labeling f is friendly}. In this paper, we determine FFI (G) for a class of cubic graphs with full vertices blow-up of cycle by a complete tripartite graph K(1, 1, 2) using a new method known as embedding labeling graph method. As a by-product, we also discuss the cordiality and the full product-cordial index sets for this graph.

• 出版日期2018-1
• 单位哈尔滨工程大学