Related papers: A Study on Integer Additive Set-Valuations of Sign…
In a signed graph $G$, an induced subgraph is called a negative clique if it is a complete graph and all of its edges are negative. In this paper, we give the characteristic polynomials and the eigenvalues of some signed graphs having…
Generalized integer splines on a graph $G$ with integer edge weights are integer vertex labelings such that if two vertices share an edge in $G$, the vertex labels are congruent modulo the edge weight. We introduce collapsing operations…
There are a variety of graphs where multidimensional feature values are assigned to the nodes. Visualization of such datasets is not an easy task since they are complex and often huge. Immersive Analytics is a powerful approach to support…
Graph-based Semi-Supervised Learning (GSSL) is a practical solution to learn from a limited amount of labelled data together with a vast amount of unlabelled data. However, due to their reliance on the known labels to infer the unknown…
A \emph{signed graph} is a pair $\Gs$ in which $G$ is a finite simple graph and $\sigma:\E(G)\to\{+1,-1\}$ is a \emph{signature}. Following M\'a\v{c}ajov\'a--Raspaud- \v{S}koviera and Jin--Kang--Steffen, a \emph{proper coloring} of $\Gs$ is…
A mixed graph is said to be HS-\emph{integral} if the eigenvalues of its Hermitian-adjacency matrix of the second kind are integers. A mixed graph is called \emph{Eisenstein integral} if the eigenvalues of its (0, 1)-adjacency matrix are…
Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, and $f$ be a 0-1 labeling of $E(G)$ so that the absolute difference in the number of edges labeled 1 and 0 is no more than one. Call such a labeling $f$ \emph{edge-friendly}. We…
A numbering $f$ of a graph $G$ of order $n$ is a labeling that assigns distinct elements of the set $\left\{ 1,2,\ldots ,n\right\} $ to the vertices of $G$. The strength $\textrm{str}_{f}\left( G\right)$ of a numbering $f:V\left( G\right)…
We say that a graph F strongly arrows a pair of graphs (G,H) if any colouring of its edges with red and blue leads to either a red G or a blue H appearing as induced subgraphs of F. The induced Ramsey number, IR(G,H) is defined as the…
Graph labeling is a technique that assigns unique labels or weights to the vertices or edges of a graph, often used to analyze and solve various graph-related problems. There are few methods with certain limitations conducted by researchers…
An antimagic labeling for a graph $G$ with $m$ edges is a bijection $f: E(G) \to \{1, 2, \dots, m\}$ so that $\phi_f(u) \neq \phi_f(v)$ holds for any pair of distinct vertices $u, v \in V(G)$, where $\phi_f(x) = \sum_{x \in e} f(e)$. A…
An injective coloring of a given graph G = (V, E) is a vertex coloring of G such that any two vertices with common neighbor receive distinct colors. An e-injective coloring of a graph G is a vertex coloring of G such that any two vertices…
A magic labelling of a graph $G$ with magic sum $s$ is a labelling of the edges of $G$ by nonnegative integers such that for each vertex $v\in V$, the sum of labels of all edges incident to $v$ is equal to the same number $s$. Stanley gave…
The Wiener index of a graph $W(G)$ is a well studied topological index for graphs. An outstanding problem of \v{S}olt{\'e}s is to find graphs $G$ such that $W(G)=W(G-v)$ for all vertices $v\in V(G)$, with the only known example being…
A graph is strongly perfect if every induced subgraph H has a stable set that meets every nonempty maximal clique of H. The characterization of strongly perfect graphs by a set of forbidden induced subgraphs is not known. Here we provide…
Active learning (AL) on attributed graphs has received increasing attention with the prevalence of graph-structured data. Although AL has been widely studied for alleviating label sparsity issues with the conventional non-related data, how…
The unitary addition Cayley graph $G_n$, $n\in Z^+$ is the graph whose vertex set is $Z_n$, the ring of integers modulo $n$ and two vertices $u$ and $v$ are adjacent if and only if $u + v \in \cup_n$ where $\cup_n$ is the set of all units…
The status of a vertex $x$ in a graph is the sum of the distances between $x$ and all other vertices. Let $G$ be a connected graph. The status sequence of $G$ is the list of the statuses of all vertices arranged in nondecreasing order. $G$…
Signed graphs are graphs with signed edges. They are commonly used to represent positive and negative relationships in social networks. While balance theory and clusterizable graphs deal with signed graphs to represent social interactions,…
A Group Labeled Graph is a pair $(G,\Lambda)$ where $G$ is an oriented graph and $\Lambda$ is a mapping from the arcs of $G$ to elements of a group. A (not necessarily directed) cycle $C$ is called non-null if for any cyclic ordering of the…