Related papers: Signed Distance in Signed Graphs
In this paper, we look into Signed Product Cordial Labeling for Splitting Graphs of Bull graph and Splitting graph of Star graph , Square of Path graph, Coronaand also for the graph obtained by joining two copies of Helm by a Path of…
A graph is a split graph if its vertex set can be partitioned into a clique and a stable set. A split graph is unbalanced if there exist two such partitions that are distinct. Cheng, Collins and Trenk (2016), discovered the following…
A {\em faithful (unit) distance graph} in $\mathbb{R}^d$ is a graph whose set of vertices is a finite subset of the $d$-dimensional Euclidean space, where two vertices are adjacent if and only if the Euclidean distance between them is…
Signed networks, characterized by edges labeled as either positive or negative, offer nuanced insights into interaction dynamics beyond the capabilities of unsigned graphs. Central to this is the task of identifying the maximum balanced…
Message-passing Graph Neural Networks (GNNs), which collect information from adjacent nodes achieve dismal performance on heterophilic graphs. Various schemes have been proposed to solve this problem, and propagating signed information on…
Like Graph Neural Networks (GNNs), Signed Graph Neural Networks (SGNNs) are also up against fairness issues from source data and typical aggregation method. In this paper, we are pioneering to make the investigation of fairness in SGNNs…
The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.
A signed graph is a graph $G$ associated with a mapping $\sigma: E(G)\to \{-1,+1\}$, denoted by $(G,\sigma)$. A $cycle$ of $(G,\sigma)$ is a connected 2-regular subgraph. A cycle $C$ is $positive$ if it has an even number of negative edges,…
A weighing matrix $W$ is quasi-balanced if $|W||W|^\top=|W|^\top|W|$ has at most two off-diagonal entries, where $|W|_{ij}=|W_{ij}|$. A quasi-balanced weighing matrix $W$ signs a strongly regular graph if $|W|$ coincides with its adjacency…
For a connected graph, the distance spectral radius is the largest eigenvalue of its distance matrix, and the distance energy is defined as the sum of the absolute values of the eigenvalues of its distance matrix. We establish lower and…
Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite…
The walk distances in graphs are defined as the result of appropriate transformations of the $\sum_{k=0}^\infty(tA)^k$ proximity measures, where $A$ is the weighted adjacency matrix of a graph and $t$ is a sufficiently small positive…
We present enumeration results on the number of connected graphs up to 10 vertices for which there is at least one other graph with the same spectrum (a cospectral mate), or at least one other graph with the same Smith normal form…
We introduce a notion of a girth-regular graph as a $k$-regular graph for which there exists a non-descending sequence $(a_1, a_2, \dots, a_k)$ (called the signature) giving, for every vertex $u$ of the graph, the number of girth cycles the…
A connected graph is called a multi-block graph if each of its blocks is a complete multi-partite graph. Building on the work of \cite{Bp3,Hou3}, we compute the determinant and inverse of the distance matrix for a class of multi-block…
A signed graph product is defined for a new product, and initially the unsigned graph product's Laplacian spectrum and signless Laplacian spectrum are found. Next, for the signed graph product, the adjacency spectrum, Laplacian spectrum,…
Highly-regular graphs can be regarded as a combinatorial generalization of distance-regular graphs. From this standpoint, we study combinatorial aspects of highly-regular graphs. As a result, we give the following three main results in this…
We characterize all connected graphs with second distance eigenvalue less than $-0.5858$.
The generalized distance matrix of a graph is the matrix whose entries depend only on the pairwise distances between vertices, and the generalized distance spectrum is the set of eigenvalues of this matrix. This framework generalizes many…
Let $k, d$ ($2d \leq k)$ be two positive integers. We generalize the well studied notions of $(k,d)$-colorings and of the circular chromatic number $\chi_c$ to signed graphs. This implies a new notion of colorings of signed graphs, and the…