We prove that, with one exception, each (n, n)-graph G that is embeddable in its complement has a self-complementary supergraph of order n. © 2005 Elsevier B.V. All rights reserved.

We compute the elementary divisors of the adjacency and Laplacian matrices of the Grassmann graph on 2-dimensional subspaces in a finite vector space. We also compute the corresponding invariants of the complementary graphs.

In this note we prove that a self-complementary graph with p vertices is chordal if and only if its clique number is integral part of (p + 1)/2. (~) 1998 Elsevier Science B.V. All rights reserved

A set D of a graph G = (V,E) is a dominating set if every vertex in V −D is adjacent to some vertex in D. The domination number γ(G) of G is the minimum cardinality of a dominating set. A dominating set D is called a complementary tree dominating set if the induced subgraph < V −D > is a tree. The minimum cardinality of a complementary tree dominating set is called the complementary tree domina...

let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...

We give a method to construct cospectral graphs for the normalized Laplacian by a local modification in some graphs with special structure. Namely, under some simple assumptions, we can replace a small bipartite graph with a cospectral mate without changing the spectrum of the entire graph. We also consider a related result for swapping out biregular bipartite graphs for the matrix A + tD. We p...

Locally-biased graph algorithms are algorithms that attempt to find local or small-scale structure in a typically large data graph. In some cases, this can be accomplished by adding some sort of locality constraint and calling a traditional graph algorithm; but more interesting are locally-biased graph algorithms that compute answers by running a procedure that does not even look at most of the...

In this paper, we develop methods to “sample” a small realistic graph from a large real network. Despite recent activity, the modeling and generation of realistic graphs is still not a resolved issue. All previous work has attempted to grow a graph from scratch. We address the complementary problem of shrinking a graph. In more detail, this work has three parts. First, we propose a number of re...

Graph-based multi-view clustering aiming to obtain a partition of data across multiple views, has received considerable attention in recent years. Although great efforts have been made for graph-based clustering, it is still challenging fuse characteristics from various views learn common representation clustering. In this paper, we propose novel Consistent Multiple Graph Embedding Clustering f...

Vertices x and y dominate a tournament T if for all vertices z 6 = x; y; either x beats z or y beats z. Let dom(T) be the graph on the vertices of T with edges between pairs of vertices that dominate T. We show dom(T) is either an odd cycle with possible pendant vertices or a forest of caterpillars. Since dom(T) is the complement of the competition graph of the tournament formed by reversing th...