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Abstract A restrained Italian dominating function (RID-function) on a graph is a function satisfying: (i) for every vertex with , where is the set of vertices adjacent to u; (ii) the subgraph induced by the vertices assigned 0 under f has no isolated vertices. The weight of an RID-function...
Abstract In this paper we show that if G is a connected graph such that , and then exists and if and only if G is not super- . We also obtain some other results.
Abstract Let G be a connected simple graph with n vertices. The distance Laplacian matrix is defined as , where is the diagonal matrix of vertex transmissions and is the distance matrix of G. The eigenvalues of are the distance Laplacian eigenvalues of G and are denoted by . The largest...
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