DISTANCE EIGENVALUES, FORWARDING INDICES, AND DISTANCE-BASED TOPOLOGICAL INDICES OF COMPLEMENT OF TWO CIRCULANT NETWORKS

DISTANCE EIGENVALUES, FORWARDING INDICES, AND DISTANCE-BASED TOPOLOGICAL INDICES OF COMPLEMENT OF TWO CIRCULANT NETWORKS

J. R. M. Antalan, F. J. H. Campena

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Abstract

Let n, a, h, and m be positive integers such that 2   a   n 2 and m   2. In this research, we compute the exact value of the distance spectral radius, vertexforwarding index, and some distance-based topological indices of the connected complement of circulant networks Cn(1; a) and Cn=mh(1; m;m2; : : : ;mh1). For a 6= n 2 , the circulant network Cn(1; a) is called a double loop network while the circulant network Cn=mh(1; m;m2; : : : ;mh1) is called the multiplicative circulant network on mh vertices.

Keywords

Circulant networks, double loop network, multiplicative circulant graph, graph complement.