Related papers: Further Results on Signed Product Cordial Labeling
A split graph is a graph whose vertices can be partitioned into a clique and a stable set. We investigate the combinatorial species of split graphs, providing species-theoretic generalizations of enumerative results due to B\'ina and…
In a signed graph, each link is labeled with either a positive or a negative sign. This is particularly appropriate to model polarized systems. Such a graph can be characterized through the notion of structural balance, which relies on the…
This paper deals with the $\lambda$-labeling and $L(2,1)$-coloring of simple graphs. A $\lambda$-labeling of a graph $G$ is any labeling of the vertices of $G$ with different labels such that any two adjacent vertices receive labels which…
A graph is closed when its vertices have a labeling by [n] with a certain property first discovered in the study of binomial edge ideals. In this article, we explore various aspects of closed graphs, including the number of closed labelings…
In the context of distributed certification, the recognition of graph classes has started to be intensively studied. For instance, different results related to the recognition of planar, bounded tree-width and $H$-minor free graphs have…
This paper studies the circular coloring of signed graphs. A signed graph is a graph with a signature that assigns a sign to each edge, either positive or negative. This paper studies circular coloring and a circular chromatic number of…
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…
In this note we show that any embedded graph has a checkerboard colourable twisted dual and any Eulerian embedded graph has a checkerboard colourable partial Petrial, answering questions posed by Ellis-Monaghan and Moffatt. The proofs are…
A signed graph is a graph whose edges are labeled either positive or negative. Corresponding to the two signed distance matrices defined for signed graphs, we define two signed distance laplacian matrices. We characterize balance in signed…
An edge uv in a graph \Gamma\ is directionally 2-signed (or, (2,d)-signed) by an ordered pair (a,b), a,b in {+,-}, if the label l(uv) = (a,b) from u to v, and l(vu) = (b,a) from v to u. Directionally 2-signed graphs are equivalent to…
In this paper, we extend our earlier proposal of corona product of signed graphs into generalized corona product of signed graphs inspired by the generalized corona product of unsigned graphs. Then we study structural balance and spectral…
A signed graph is a pair $(G, \sigma)$, where $G$ is a graph and $\sigma: E(G) \to \{+, -\}$ is a signature which assigns to each edge of $G$ a sign. Various notions of coloring of signed graphs have been studied. In this paper, we extend…
We introduce a new subclass of chordal graphs that generalizes split graphs, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set into cliques that can be arranged in a star…
A signed graph has edge signs. A gain graph has oriented edge gains drawn from a group. We define the combination of the two for the abelian case, in which each oriented edge of a signed graph has a gain from an abelian group, concentrating…
This paper surveys recent development of concepts related to coloring of signed graphs. Various approaches are presented and discussed.
We study additively graceful labelings of signed graphs on stars and double stars. While the case of signed stars is straightforward, the problem becomes significantly more intricate for signed double stars. We obtain a characterization of…
A signed graph (SG) is a graph where edges carry sign information attached to it. The sign of a network can be positive, negative, or neutral. A signed network is ubiquitous in a real-world network like social networks, citation networks,…
We extend the work of Hanlon on the chromatic polynomial of an unlabeled graph to define the unlabeled chromatic polynomial of an unlabeled signed graph. Explicit formulas are presented for labeled and unlabeled signed chromatic polynomials…
In this paper we determine the signed Roman domination number of the join of cycles, wheels, fans and friendship graphs.
The splitting number is effective to distinguish the embedded topology of plane curves, and it is not determined by the fundamental group of the complement of the plane curve. In this paper, we give a generalization of the splitting number,…