The eccentric weight of graphs (Q1698499)

Summary: Let \(G=(V,E)\) be a connected graph. The eccentricity \(e(u)\) of a vertex \(u\in V(G)\), is the maximum distance from it to another vertex of \(G\). The eccentric wight of \(G\), \(ew(G)\), is defined as \(\sum\limits_{x\in E}f(x)\), where \(f:E\longrightarrow \{0,1\}\) is a function and \(f(uv)=|e(u)-e(v)|\) for all \(uv\in E(G)\). In this paper, we compute the eccentric weight of several classes of graphs. Some bounds for \(ew(G)\) are established. The eccentric weight of join and Cartesian product of graphs are obtained.