Bounds on the distinguishing chromatic number.
-groups.
Cacti, braids and complex polynomials.
Canonical characters on simple graphs
A multiplicative functional on a graded connected Hopf algebra is called the character. Every character decomposes uniquely as a product of an even character and an odd character. We apply the character theory of combinatorial Hopf algebras to the Hopf algebra of simple graphs. We derive explicit formulas for the canonical characters on simple graphs in terms of coefficients of the chromatic symmetric function of a graph and of canonical characters on quasi-symmetric functions. These formulas and...
Cayley color graphs of inverse semigroups and groupoids
The notion of Cayley color graphs of groups is generalized to inverse semigroups and groupoids. The set of partial automorphisms of the Cayley color graph of an inverse semigroup or a groupoid is isomorphic to the original inverse semigroup or groupoid. The groupoid of color permuting partial automorphisms of the Cayley color graph of a transitive groupoid is isomorphic to the original groupoid.
Cayley graphs on the symmetric group generated by initial reversals have unit spectral gap.
Characterization by intersection graph of some families of finite nonsimple groups
For a finite group , , the intersection graph of , is a simple graph whose vertices are all nontrivial proper subgroups of and two distinct vertices and are adjacent when . In this paper, we classify all finite nonsimple groups whose intersection graphs have a leaf and also we discuss the characterizability of them using their intersection graphs.
Characterization of finite groups by their commuting graph.
Characterization of simple orbit graphs.
Characterization of by its non-commuting graph.
Chiral hypermaps with few hyperfaces
Chordal intersection graphs of bands
Classification of rings with toroidal Jacobson graph
Let be a commutative ring with nonzero identity and the Jacobson radical of . The Jacobson graph of , denoted by , is defined as the graph with vertex set such that two distinct vertices and are adjacent if and only if is not a unit of . The genus of a simple graph is the smallest nonnegative integer such that can be embedded into an orientable surface . In this paper, we investigate the genus number of the compact Riemann surface in which can be embedded and explicitly...
Cliques and Claws in Edge-transitive Strongly Regular Graphs.
Closed walks in coset graphs and vertex-transitive non-Cayley graphs.
Cohomology with free coefficients of the fundamental group of a graph of groups.
Color Energy Of A Unitary Cayley Graph
Let G be a vertex colored graph. The minimum number χ(G) of colors needed for coloring of a graph G is called the chromatic number. Recently, Adiga et al. [1] have introduced the concept of color energy of a graph Ec(G) and computed the color energy of few families of graphs with χ(G) colors. In this paper we derive explicit formulas for the color energies of the unitary Cayley graph Xn, the complement of the colored unitary Cayley graph (Xn)c and some gcd-graphs.
Commuting graphs for partially commutative nilpotent -groups of class 2.
Comparing a Cayley digraph with its reverse.
Completely 0-simple semigroups and their associated graphs and groups.