Related papers: Representing split graphs by words
We introduce Clique Matrices as an alternative representation of undirected graphs, being a generalisation of the incidence matrix representation. Here we use clique matrices to decompose a graph into a set of possibly overlapping clusters,…
A graph is said to be well-dominated if all its minimal dominating sets are of the same size. The class of well-dominated graphs forms a subclass of the well studied class of well-covered graphs. While the recognition problem for the class…
A distinguishing coloring of a graph is a vertex coloring such that only the identity automorphism of the graph preserves the coloring. A 2-distinguishable graph is a graph which can be distinguished using 2 colors. The cost $\rho(G)$ of a…
We associate all small subgraph counting problems with a systematic graph encoding/representation system which makes a coherent use of graphlet structures. The system can serve as a unified foundation for studying and connecting many…
Mining graph data has become a popular research topic in computer science and has been widely studied in both academia and industry given the increasing amount of network data in the recent years. However, the huge amount of network data…
The simplex graph $S(G)$ of a graph $G$ is defined as the graph whose vertices are the cliques of $G$ (including the empty set), with two vertices being adjacent if, as cliques of $G$, they differ in exactly one vertex. Simplex graphs form…
A graph $G$ is perfectly divisible if every induced subgraph $H$ of $G$ contains a set $X$ of vertices such that $X$ meets all largest cliques of $H$, and $X$ induces a perfect graph. The chromatic number of a perfectly divisible graph $G$…
A subset $X$ of vertices in a graph $G$ is a {\em diameter 2 subset} if the distance of any two vertices of $X$ is at most two {\em in $G[X]$}. Relaxing this notion, a subset $X$ of vertices in a graph $G$ is a {\em 2-reachable subset} if…
We investigate inflection structure of a synthetic language using Latin as an example. We construct a bipartite graph in which one group of vertices correspond to dictionary headwords and the other group to inflected forms encountered in a…
Bipartite graphs model the relationship between two disjoint sets of objects. They have a wide range of applications and are often visualized as a 2-layered drawing, where each set of objects is visualized as a set of vertices (points) on…
A graph is perfectly divisible if for each of its induced subgraph $H$, $V(H)$ can be partitioned into $A$ and $B$ such that $H[A]$ is perfect and $\omega(H[B]) < \omega(H)$, and a graph $G$ is perfectly weight divisible if for every…
In this paper we develop three characterizations for isomorphism of graphs. The first characterization is obtained by associating certain bitableaux with the graphs. We order these bitableaux by suitably defined lexicographic order and…
We investigate the relationship between the lexicographic product of graphs and their multi-word-representation number. We establish bounds on the multi-word-representation number $\mu$ for lexicographic powers and products. Specifically,…
Many models learn representations of knowledge graph data by exploiting its low-rank latent structure, encoding known relations between entities and enabling unknown facts to be inferred. To predict whether a relation holds between…
In this paper we study the practicality and usefulness of incorporating distributed representations of graphs into models within the context of drug pair scoring. We argue that the real world growth and update cycles of drug pair scoring…
In Linguistics, a grapheme is a written unit of a writing system corresponding to a phonological sound. In Natural Language Processing tasks, written language is analysed through two different mediums, word analysis, and character analysis.…
Community detection in graphs is a problem that is likely to be relevant whenever network data appears, and consequently the problem has received much attention with many different methods and algorithms applied. However, many of these…
Graph problems are fundamentally challenging for large language models (LLMs). While LLMs excel at processing unstructured text, graph tasks require reasoning over explicit structure, permutation invariance, and computationally complex…
Graphs are a powerful tool for representing and analyzing complex relationships in real-world applications such as social networks, recommender systems, and computational finance. Reasoning on graphs is essential for drawing inferences…
Graph is a universe data structure that is widely used to organize data in real-world. Various real-word networks like the transportation network, social and academic network can be represented by graphs. Recent years have witnessed the…