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The metric dimension beta(G) (Tillquist et al. 2021) or dim(G) (Tomescu and Javid 2007, Ali et al. 2016) of a graph G is the smallest number of nodes required to identify all ...

A topology that is "potentially" a metric topology, in the sense that one can define a suitable metric that induces it. The word "potentially" here means that although the ...

The Nagel line is the term proposed for the first time in this work for the line on which the incenter I, triangle centroid G, Spieker center Sp, and Nagel point Na lie. ...

"The" octahedral graph is the 6-node 12-edge Platonic graph having the connectivity of the octahedron. It is isomorphic to the circulant graph Ci_6(1,2), the cocktail party ...

If perpendiculars A^', B^', and C^' are dropped on any line L from the vertices of a triangle DeltaABC, then the perpendiculars to the opposite sides from their perpendicular ...

d_n=p_(n+1)-p_n. (1) The first few values are 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, ... (OEIS A001223). Rankin has shown that d_n>(clnnlnlnnlnlnlnlnn)/((lnlnlnn)^2) ...

A quasi-cubic graph is a quasi-regular graph, i.e., a graph such that degree of every vertex is the same delta except for a single vertex whose degree is Delta=delta+1 ...

The operation of exchanging all points of a mathematical object with their mirror images (i.e., reflections in a mirror). Objects that do not change handedness under ...

Two nonisomorphic graphs that have equal resistance spectra (i.e., multisets of resistance distances) are said to be resistance-equivalent. All nonisomorphic simple graphs on ...

Consider a network of n resistors R_i so that R_2 may be connected in series or parallel with R_1, R_3 may be connected in series or parallel with the network consisting of ...