1. CMB 2014 (vol 57 pp. 573)
|Some Results on the Domination Number of a Zero-divisor Graph|
In this paper, we investigate the domination, total domination and semi-total domination numbers of a zero-divisor graph of a commutative Noetherian ring. Also, some relations between the domination numbers of $\Gamma(R/I)$ and $\Gamma_I(R)$, and the domination numbers of $\Gamma(R)$ and $\Gamma(R[x,\alpha,\delta])$, where $R[x,\alpha,\delta]$ is the Ore extension of $R$, are studied.
Keywords:zero-divisor graph, domination number
2. CMB 2014 (vol 57 pp. 520)
|Maximizing the Index of Trees with Given Domination Number|
The index of a graph $G$ is the maximum eigenvalue of its adjacency matrix $A(G)$. In this paper we characterize the extremal tree with given domination number that attains the maximum index.
Keywords:trees, spectral radius, index, domination number