شماره ركورد كنفرانس :
5263
عنوان مقاله :
Two modifications of Zagreb indices under some graph operations
پديدآورندگان :
Falahati Nezhad Farzaneh farzanehfalahati_n@yahoo.com Department of Mathematics, Safadasht Branch, Islamic Azad University, Tehran, Iran , Dehgardi Nasrin n.dehgardi@sirjantech.ac.ir Department of Mathematics and Computer Science, Sirjan University of Technology, Sirjan, Iran , Azari Mahdieh mahdie.azari@gmail.com Department of Mathematics, Kazerun Branch, Islamic Azad University, P. O. Box: 73135-168, Kazerun, Iran
كليدواژه :
Graph invariants , graph operations , vertex degree , upper bound
عنوان كنفرانس :
54 امين كنفرانس رياضي ايران
چكيده فارسي :
The modified Zagreb indices of a nontrivial simple connected graph $A$ are formulated by $$^mM_1(A)=sum_{ain V_A}frac{1}{d^2_{A}(a)}~~{m{and}}~~ ^mM_2(A)=sum_{e=abin E_A}frac{1}{d_{A}(a)d_{A}(b)},$$ where $V_A$, $E_A$ and $d_{A}(a)$ stand for the vertex set of $A$, edge set of $A$ and degree of $a$ in $A$, respectively. In this paper, we obtain upper bounds on the modified Zagreb indices of some graph operations including join, corona product, Cartesian product and lexicographic product of graphs.
