Abstract
For a graph G without isolated vertices, the inverse degree of a graph G is defined as ID(G) = ∑u2V(G) d(u)-1 where d(u) is the number of vertices adjacent to the vertex u in G. By replacing-1 by any non-zero real number we obtain zeroth-order general Randic index, i.e., 0Rγ(G) = ∑u2V(G) d(u)γ, where γ ∈ R-System. Text. UTF8Encoding. Xu et al. investigated some lower and upper bounds on ID for a connected graph γ in terms of connectivity, chromatic number, number of cut edges, and clique number. In this paper, we extend their results and investigate if the same results hold for γ < 0. The corresponding extremal graphs have also been identified.
Original language | English |
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Article number | 98 |
Journal | Mathematics |
Volume | 8 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jan 1 2020 |
Keywords
- Extremal graphs
- Graph parameters
- Inverse degree
- Zeroth order general Randic index
ASJC Scopus subject areas
- Computer Science (miscellaneous)
- Engineering (miscellaneous)
- General Mathematics