1. Some extremal results on the connective eccentricity index of graphs.
- Author
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Xu, Kexiang, Das, Kinkar Ch., and Liu, Haiqiong
- Subjects
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GRAPH theory , *GEOMETRIC vertices , *MEASUREMENT of angles (Geometry) , *INVARIANTS (Mathematics) , *NUMBER theory - Abstract
The connective eccentricity index (CEI) of a graph G is defined as ξ ce ( G ) = ∑ v i ∈ V ( G ) d ( v i ) ε ( v i ) where ε ( v i ) and d ( v i ) are the eccentricity and the degree of vertex v i , respectively, in G . In this paper we obtain some lower and upper bounds on the connective eccentricity index for all trees of order n and with matching number β and characterize the corresponding extremal trees. And the maximal graphs of order n and with matching number β and n edges have been determined which maximize the connective eccentricity index. Also the extremal graphs with maximal connective eccentricity index are completely characterized among all connected graphs of order n and with matching number β . Moreover we establish some relations between connective eccentricity index and eccentric connectivity index, as another eccentricity-based invariant, of graphs. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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