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), 1994-2004 and n-(D) denote the number of positive, 0, and negative eigenvalues of D, respectively.In this paper, we mainly study the inertia of distance matrices of some VITAMIN C CRYSTALS graphs related to wheel graphs and give a construction for graphs whose distance matrices have exactly one positive eigenvalue.