Related papers: On Index coding for Complementary Graphs with focu…
Motivated by the concept of well-covered graphs, we define a graph to be well-bicovered if every vertex-maximal bipartite subgraph has the same order (which we call the bipartite number). We first give examples of them, compare them with…
A graph is called matching covered if for its every edge there is a maximum matching containing it. It is shown that minimal matching covered graphs contain a perfect matching.
This paper studies the problem of broadcasting in synchronous point-to-point networks, where one initiator owns a piece of information that has to be transmitted to all other vertices as fast as possible. The model of fractional dynamic…
The problem of computing a linear combination of sources over a multiple access channel is studied. Inner and outer bounds on the optimal tradeoff between the communication rates are established when encoding is restricted to random…
Cayley graph techniques are introduced for the problem of constructing networks having the maximum possible number of nodes, among networks that satisfy prescribed bounds on the parameters maximum node degree and broadcast diameter. The…
A proper edge coloring of a graph $G$ with colors $1,2,\dots,t$ is called a cyclic interval $t$-coloring if for each vertex $v$ of $G$ the edges incident to $v$ are colored by consecutive colors, under the condition that color $1$ is…
The restricted hypercube-like graphs, variants of the hypercube, were proposed as desired interconnection networks of parallel systems. The matching preclusion number of a graph is the minimum number of edges whose deletion results in the…
If $\Gamma$ is a graph for which every edge is in exactly one clique of order $\omega$, then one can form a new graph with vertex set equal to these cliques. This is a generalization of the line graph of $\Gamma$. We discover many general…
We investigate the structure of conformally rigid graphs. Graphs are conformally rigid if introducing edge weights cannot increase (decrease) the second (last) eigenvalue of the Graph Laplacian. Edge-transitive graphs and distance-regular…
A strong edge-coloring of a graph $G$ is a coloring of the edges such that every color class induces a matching in $G$. The strong chromatic index of a graph is the minimum number of colors needed in a strong edge-coloring of the graph. In…
The zero-divisor graph of a finite commutative ring with unity is the graph whose vertex set is the set of zero-divisors in the ring, with $a$ and $b$ adjacent if $ab=0$. We show that the class of zero-divisor graphs is universal, in the…
A perfect code in a graph $\Gamma$ is a subset $C$ of $V(\Gamma)$ such that no two vertices in $C$ are adjacent and every vertex in $V(\Gamma)\setminus C$ is adjacent to exactly one vertex in $C$. Let $G$ be a finite group and $C$ a subset…
The chordal ring (CR) graphs are a well-known family of graphs used to model some interconnection networks for computer systems in which all nodes are in a cycle. Generalizing the CR graphs, in this paper, we introduce the families of…
In a graph $\Gamma$, a perfect code is an independent set $C$ with the property that every vertex not in $C$ is adjacent to a unique vertex in $C$, and a total perfect code is a set $C$ of vertices of $\Gamma$ such that every vertex of…
The class of quasi-chain graphs is an extension of the well-studied class of chain graphs. This latter class enjoys many nice and important properties, such as bounded clique-width, implicit representation, well-quasi-ordering by induced…
The degree distribution of a graph $G=(V,E)$, $|V|=n$, $|E|=m$ is one of the most fundamental objects of study in the analysis of graphs as it embodies relationship among entities. In particular, an important derived distribution from…
The biclique cover number $(\text{bc})$ of a graph $G$ denotes the minimum number of complete bipartite (biclique) subgraphs to cover all the edges of the graph. In this paper, we show that $\text{bc}(G) \geq \lceil \log_2(\text{mc}(G^c))…
A vertex colouring of some graph is called perfect if each vertex of colour $i$ has exactly $a_{ij}$ neighbours of colour $j$. Being perfect imposes several restrictions on the colour incidence matrix $(a_{ij})$. We list several (old and…
The problem of counting occurrences of query graphs in a large data graph, known as subgraph counting, is fundamental to several domains such as genomics and social network analysis. Many important special cases (e.g. triangle counting)…
We consider the function computation problem in a three node network with one encoder and two decoders. The encoder has access to two correlated sources $X$ and $Y$. The encoder encodes $X^n$ and $Y^n$ into a message which is given to two…