On the Zagreb indices of graphs with given Roman domination number

Communications in Combinatorics and Optimization

article

Ayu Ameliatul Shahilah Ahmad Jamri¹  Roslan Hasni²  Sharifah Kartini Said Husain³ 

[1] MENGGABANG TELIPOT KUALA NERUS;Universiti Malaysia Terengganu;Universiti Putra Malaysia

关键词: Zagreb index;    Roman domination number;    tree;   

DOI  :  10.22049/cco.2021.27439.1263

学科分类：社会科学、人文和艺术（综合）

来源: Azarbaijan Shahide Madani Universit

【 摘 要 】

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$. The two Zagreb indices $M_1=\sum_{v\in V(G)} d^2_G(v)$ and $M_2=\sum_{uv\in E(G)} d_G(u)d_G(v)$ 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.

【 授权许可】

CC BY-SA