5 research outputs found
The hyper-Wiener index of the generalized hierarchical product of graphs
AbstractThe hyper Wiener index of the connected graph G is WW(G)=12∑{u,v}⊆V(G)(d(u,v)+d(u,v)2), where d(u,v) is the distance between the vertices u and v of G. In this paper we compute the hyper-Wiener index of the generalized hierarchical product of two graphs and give some applications of this operation
The vertex PI index and Szeged index of bridge graphs
AbstractRecently the vertex Padmakar–Ivan (PIv) index of a graph G was introduced as the sum over all edges e=uv of G of the number of vertices which are not equidistant to the vertices u and v. In this paper the vertex PI index and Szeged index of bridge graphs are determined. Using these formulas, the vertex PI indices and Szeged indices of several graphs are computed
The Total Irregularity of Graphs under Graph Operations
The total irregularity of a graph is defined as \irr_t(G)=1/2 \sum_{u,v
\in V(G)} , where denotes the degree of a vertex . In this paper we give (sharp) upper bounds on the total irregularity
of graphs under several graph operations including join, lexicographic product,
Cartesian product, strong product, direct product, corona product, disjunction
and symmetric difference.Comment: 14 pages, 3 figures, Journal numbe