The Distance Matrices of Some Graphs Related to Wheel Graphs

The Distance Matrices of Some Graphs Related to Wheel Graphs

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Let D denote the distance matrix of a connected graph G.The inertia of D is the triple of integers (n+(D), n0(D), n-(D)), where n+(D), n0(D), Dryer Decal and n-(D) denote the number of positive, 0, and negative eigenvalues of D, respectively.In this paper, we mainly 407 study the inertia of distance matrices of some graphs related to wheel graphs and give a construction for graphs whose distance matrices have exactly one positive eigenvalue.