Author/Authors :
Ahmad Jamri, Ayu Ameliatul Shahilah Special Interest Group on Modeling and Data Analytics (SIGMDA) - Faculty of Ocean Engineering Technology and Informatics - Universiti Malaysia Terengganu - Kuala Nerus, Terengganu, Malaysia , Hasni, Roslan Special Interest Group on Modeling and Data Analytics (SIGMDA) - Faculty of Ocean Engineering Technology and Informatics - Universiti Malaysia Terengganu - Kuala Nerus, Terengganu, Malaysia , Said Husain, Sharifah Kartini Department of Mathematics and Statistics - Faculty of Science - Universiti Putra Malaysia - Serdang, Selangor, Malaysia - Laboratory of Cryptography - Analysis and Structure - Institute for Mathematical Research (INSPEM) - Universiti Putra Malaysia - Serdang, Selangor, Malaysia
Abstract :
Let G be a graph with vertex set V(G) and edge set E(G). The two Zagreb indices M1=∑v∈V(G)d2G(v) and M2=∑uv∈E(G)dG(u)dG(v) are vertex degree based graph invariants that have been introduced in the 1970s and extensively studied ever since. {In this paper, we first give a lower bound on the first Zagreb index of trees with given Roman domination number and we characterize all extremal trees. Then we present upper bound for Zagreb indices of unicyclic and bicyclic graphs with given Roman domination number.
Keywords :
Zagreb index , Roman domination number , tree , unicyclic graph , bicyclic graph
