Extremal Edge General Position Sets in Some Graphs

A set of edges X subset of E ( G ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X\subseteq E(G)$$\end{document} of a graph G is an edge general position set if no three edges from X lie on a common shortest path. The edge general position number gp e ( G ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textrm{gp}}_{\textrm{e}}(G)$$\end{document} of G is the cardinality of a largest edge general position set in G. Graphs G with gp e ( G ) = | E ( G ) | - 1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textrm{gp}}_{{\textrm{e}}}(G) = |E(G)| - 1$$\end{document} and with gp e ( G ) = 3 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textrm{gp}}_{{\textrm{e}}}(G) = 3$$\end{document} are respectively characterized. Sharp upper and lower bounds on gp e ( G ) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textrm{gp}}_{{\textrm{e}}}(G)$$\end{document} are proved for block graphs G and exact values are determined for several specific block graphs.