On the maximal distance spectral radius in a class of bicyclic graphs. (English) Zbl 1257.05087
Summary: Bicyclic graphs are connected graphs in which the number of edges equals the number of vertices plus one. Let \(P_{p+1} = x_1x_2 \cdots x_{p+1}, P_{t+1} = y_1y_2\cdots y_{t+1}\) and \(P{q+1} = z_1z_2\cdots z_{q+1}\) be three vertex-disjoint paths. Identifying the initial vertices as \(u_0\) and the terminal vertices as \(v_0\), the resultant graph, denoted by \(\theta(p; t; q)\), is called a \(\theta\)-graph. Let \(\mathcal B_n\) be the class of all bicyclic graphs on \(n\) vertices, which contain a \(\theta\)-graph as an induced subgraph.
In this paper, we study the distance spectral radius of bicyclic graphs in \(\mathcal B_n\), and determine the graph with the largest distance spectral radius.
In this paper, we study the distance spectral radius of bicyclic graphs in \(\mathcal B_n\), and determine the graph with the largest distance spectral radius.
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