Pairwise compatibility graphs: A survey

T Calamoneri, B Sinaimeri - siam REVIEW, 2016 - SIAM
A graph G=(V,E) is a pairwise compatibility graph (PCG) if there exists an edge-weighted
tree T and two nonnegative real numbers d_min and d_max such that each leaf u of T is a …

All graphs with at most seven vertices are pairwise compatibility graphs

T Calamoneri, D Frascaria, B Sinaimeri - The Computer Journal, 2013 - academic.oup.com
A graph G is called a pairwise compatibility graph (PCG) if there exists an edge-weighted
tree T and two non-negative real numbers d min and d max such that each leaf lu of T …

A survey on pairwise compatibility graphs

MS Rahman, S Ahmed - AKCE International Journal of Graphs and …, 2020 - Taylor & Francis
Let T be an edge weighted tree and dmin, dmax be two non-negative real numbers where d
min≤ d max. The pairwise compatibility graph (PCG) of T for dmin, dmax is a graph G such …

On 2-interval pairwise compatibility properties of two classes of grid graphs

BB Papan, PB Pranto, MS Rahman - The Computer Journal, 2023 - academic.oup.com
A graph is called a pairwise compatibility graph (PCG) if it admits a tuple of an edge-
weighted tree of non-negative edge weights with leaf set, two non-negative real numbers …

Characterizing star-PCGs

M **ao, H Nagamochi - Algorithmica, 2020 - Springer
A graph G is called a pairwise compatibility graph (PCG, for short) if it admits a tuple (T, w,
d_\min, d_\max)(T, w, d min, d max) of a tree T whose leaf set is equal to the vertex set of G …

[HTML][HTML] Exact-2-relation graphs

Y Long, PF Stadler - Discrete Applied Mathematics, 2020 - Elsevier
Pairwise compatibility graphs (PCGs) with non-negative integer edge weights recently have
been used to describe rare evolutionary events and scenarios with horizontal gene transfer …

A method for enumerating pairwise compatibility graphs with a given number of vertices

NA Azam, A Shurbevski, H Nagamochi - Discrete Applied Mathematics, 2021 - Elsevier
Abstract Azam et al.(2018) proposed a method to enumerate all pairwise compatibility
graphs (PCGs) with a given number n of vertices. For a tuple (G, T, σ, λ) of a graph G with n …

New results on pairwise compatibility graphs

SA Hakim, BB Papan, MS Rahman - Information Processing Letters, 2022 - Elsevier
Abstract A graph G=(V, E) is called a pairwise compatibility graph (PCG) if there exists an
edge-weighted tree T and two non-negative real numbers dmin and dmax such that each …

Recognition of linear and star variants of leaf powers is in p

B Benjamin, S Høgemo, JA Telle… - International Workshop on …, 2022 - Springer
A k-leaf power of a tree T is a graph G whose vertices are the leaves of T and whose edges
connect pairs of leaves whose distance in T is at most k. A graph is a leaf power if it is ak-leaf …

[HTML][HTML] Some classes of graphs that are not PCGs

P Baiocchi, T Calamoneri, A Monti… - Theoretical Computer …, 2019 - Elsevier
Abstract A graph G=(V, E) is a pairwise compatibility graph (PCG) if there exists an edge-
weighted tree T and two non-negative real numbers dmin and dmax, dmin≤ dmax, such that …