ON DOMINATION NUMBER AND ECCENTRIC CONNECTIVITY INDEX OF TRANSFORMATION GRAPHS
Preeti B. Jinagouda1, Shailaja S. Shirkol2, Vidya S. Raikar3
1,2Department of Mathematics, SDM College of Engineering and Technology Dharwad, Karnataka, India
3Department of Mathematics, Govt. First Grade College Dharwad, Karnataka, India
Abstract: A set D ⊆ V is a dominating set of G if every vertex in V − D is adjacent to one or more vertices in D. The minimum cardinality of a dominating set of a graph G is called the domination number of G and is denoted by γ(G). The eccentric connectivity index is the sum of the product of eccentricity and degree of every vertex in G. In this paper, we present upper bounds for the total transformation graphs in terms of domination number and eccentric connectivity index of a graph G.
Keywords: Domination Number; eccentricity connectivity index; transformation graph.
AMS Subject Classification: 05C69;05C92.
VOLUME 10 ISSUE 06 2026: 119 – 129