2020•WSEAS TRANSACTIONS ON MATHEMATICSOpen access

Line Graphs and Middle Graphs that are Divisor Graphs

Salah Al-Addasi, Hasan Al-Ezeh, Omar A. AbuGhneim

Abstract

In this paper it is determined when the line graphs and the middle graphs of some classes of graphs are divisor graphs. Complete characterizations for cycles, trees, complete graphs and complete multipartite graphs whose line graphs (middle graphs) are divisor graphs are obtained. It is also shown that the line graphs and the middle graphs of the cycle permutation graphs are never divisor graphs.

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Available abstract

Key concepts: Indifference graph, Pathwidth, Chordal graph, Combinatorics, Trapezoid graph, 1-planar graph, Cograph, Clique-sum