Let $G$ be a graph of order $n$ with vertices labeled as $v_1, v_2,\dots , v_n$. Let $d_i$ be the degree of the vertex $v_i$ for $i = 1, 2, \cdots , n$. The Albertson matrix of $G$ is the square
چکیده کامل
Let $G$ be a graph of order $n$ with vertices labeled as $v_1, v_2,\dots , v_n$. Let $d_i$ be the degree of the vertex $v_i$ for $i = 1, 2, \cdots , n$. The Albertson matrix of $G$ is the square matrix of order $n$ whose $(i, j)$-entry is equal to $|d_i - d_j|$ if $v_i $ is adjacent to $v_j$ and zero, otherwise. The main purposes of this paper is to introduce the Albertson energy and Albertson-Estrada index of a graph, both base on the eigenvalues of the Albertson matrix. Moreover, we establish upper and lower bounds for these new graph invariants and relations between them.
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