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Color Code Techniques In Rainbow Connection

let g be a graph with an edge k-coloring γ : e(g) → {1, …, k} (not necessarily proper). a path is called a rainbow path if all of its edges have different colors. the map γ is called a rainbow colori

Domination Number of the Non-commuting Graph of Finite Groups

let g be a non-abelian group. the non-commuting graph of group g, shown by Γg, is a graph with the vertex set g \ z(g), where z(g) is the center of group g. also two distinct vertices of a and b are a...

On Topological Integer Additive Set-labeling of Star Graphs

for integer k ≥ 2, let x = {0, 1, 2, …, k}. in this paper, we determine the order of a star graph k1, n of n + 1 vertices, such that k1, n admits a topological integer additive

Interlace Polynomials of Friendship Graphs

in this paper, we study the interlace polynomials of friendship graphs, that is, graphs that satisfy the friendship theorem given by erdös, rényi and sos. explicit formulas, special values and behavio...

The Structure of Graphs with Forbidden Induced $C_4$, $\Overline{C}_4$, $C_5$, $S_3$, Chair and Co-chair

we find the structure of graphs that have no c4, $\overline{c}_4$, c5, s3, chair and co-chair as induced subgraphs. then we deduce the structure of the graphs having no induced c4, $\overline{c_4}$, s...

Parsimonious Edge-coloring on Surfaces

we correct a small error in a 1996 paper of albertson and haas, and extend their lower bound for the fraction of properly colorable edges of planar subcubic graphs that are simple, connected, bridgele...

Graphs, Friends and Acquaintances

a graph is a mathematical object modeling the existence of a certain relation between pairs of elements of a given set. many of the first results concerning graphs made reference to relationships betw...

Some Bound of the Edge Chromatic Surplus of Certain Cubic Graphs

v.g. vizing showed that any graph belongs to one of two classes: class 1 if χʹ(g) = Δ(g) or in class 2 if χʹ(g) = Δ(g) + 1, where χʹ(g) and Δ(g) denote the edge chromatic index of g an

A Note on Fibonacci and Lucas Number of Domination in Path

let g = (v(g), e(g)) be a path of order n ≥ 1. let fm(g) be a path with m ≥ 0 independent dominating vertices which follows a fibonacci string of binary numbers where 1 is the dominating vertex. a set.

Some Diameter Notions in Lexicographic Product

many graphs such as hypercubes, star graphs, pancake graphs, grid, torus etc are known to be good interconnection network topologies. in any network topology, the vertices represent the processors and...

On Distance Signless Laplacian Spectrum and Energy of Graphs

the distance signless laplacian spectral radius of a connected graph g is the largest eigenvalue of the distance signless laplacian matrix of g‎, ‎defined as ‎d‎q(g) = tr(g) + d(g)‎, ‎w

Total Vertex Irregularity Strength of Trees with Maximum Degree Five

in 2010, nurdin, baskoro, salman and gaos conjectured that the total vertex irregularity strength of any tree t is determined only by the number of vertices of degrees 1, 2 and 3 in t. this paper will...

On Regular Handicap Graphs of Order $N \Equiv 0$ Mod 8

a handicap distance antimagic labeling of a graph g = (v, e) with n vertices is a bijection f̂ : v → {1, 2, …, n} with the property that f̂(xi) = i, the weight w(xi) is the sum of labels of all neigh

Characterization of Perfect Matching Transitive Graphs

a graph g is perfect matching transitive, shortly pm-transitive, if for any two perfect matchings m and n of g, there is an automorphism f : v(g) ↦ v(g) such that fe(m) = n, where fe(uv) =

List Graphs and Distance-consistent Node Labelings

in this paper we consider node labelings c of an undirected connected graph g=(v,e) with labels {1,2,... ,|v|}, which induce a list distance c(u,v)=|c(v)-c(u)| besides the usual graph distance d(u,v)....

Ramanujan Graphs Arising as Weighted Galois Covering Graphs

we give a new construction of ramanujan graphs using a generalized type of covering graph called a weighted covering graph. for a given prime p the basic construction produces bipartite ramanujan grap...

Rainbow Perfect Domination in Lattice Graphs

let $0

Distance Matrices and Quadratic Embedding of Graphs

a connected graph is said to be of qe class if it admits a quadratic embedding in a hilbert space, or equivalently, if the distance matrix is conditionally negative definite. several criteria for a g...

On Maximum Signless Laplacian Estrada Index of Graphs with Given Parameters II

the signless laplacian estrada index of a graph $g$ is defined as $slee(g)=\sum^{n}_{i=1}e^{q_i}$ where $q_1, q_2, \ldots, q_n$ are the eigenvalues of the signless laplacian matrix of g. following th...

Upper Bounds on the Bondage Number of a Graph

the bondage number b(g) of a graph g is the smallest number of edges whose removal from g results in a graph with larger domination number. we obtain sufficient conditions for the validity of the ineq...

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