Bulletin of the Iranian Mathematical Society.

Abstract In the Maker–Breaker resolving game, two players named Resolver and Spoiler alternately select unplayed vertices of a given graph G . The aim of Resolver is to select all the vertices of some resolving set of G , while Spoiler aims to select at least one vertex from every resolving set of G . In this paper, this game is investigated on the lexicographic product of graphs. It is proved th…

Abstract For a given pair of plane curves $$(\alpha , \gamma )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>γ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , we study the symmetry of $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> with respect to $$…

Abstract The stress interval S ( u , v ) between $$u,v\in V(G)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>u</mml:mi> <mml:mo>,</mml:mo> <mml:mi>v</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>V</mml:mi> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> is the set of all vertices in a graph G that lie on every shortest u , v -path. A set $$U…