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Ratio of the number of -nearly independent vertex subsets and the Merrifield-Simmons index
Audace A. V. Dossou-Olory, Eric O. D. Andriantiana, Valisoa R. M. Rakotonarivo +1
The number of induced subgraphs with size of a graph was introduced recently as the number of -nearly independent vertex subsets of . Results highlighting si…
Characterization of Trees with Maximum Security
Alex S. A. Alochukwu, Audace A. V. Dossou-Olory, Fadekemi J. Osaye +5
The rank (also known as protection number or leaf-height) of a vertex in a rooted tree is the minimum distance between the vertex and any of its leaf descendants. We consider the s…
On minimizing the Wiener index of unicyclic graphs with fixed girth and given degree sequence
Alewyn P. Burger, Valisoa R. M. Rakotonarivo
The Wiener index of a graph is the sum of all the distances between any pair of vertices. We aim to describe graphs which minimize the Wiener index among all unicyclic graphs with…
On the Sombor index of trees with degree restrictions
Eric O. D. Andriantiana, Valisoa R. M. Rakotonarivo
We study the Sombor index of trees with various degree restrictions. In addition to rediscovering that among all trees with a given degree sequence, the greedy tree minimises the S…