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# ELECTRONIC JOURNAL OF GRAPH THEORY AND APPLICATIONS (EJGTA)

##### Color Code Techniques In Rainbow Connection

let g be a graph with an edge k-coloring Î³ : e(g) â†’ {1, â€¦, k} (not necessarily proper). a path is called a rainbow path if all of its edges have different colors. the map Î³ 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 Î“g, 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 kâ€„â‰¥â€„2, let xâ€„=â€„{0,â€†1,â€†2,â€†â€¦,â€†k}. in this paper, we determine the order of a star graph k1,â€†n of nâ€…+â€…1 vertices, such that k1,â€†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 erdÃ¶s, rÃ©nyi 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 Ï‡Ê¹(g)â€„=â€„Î”(g) or in class 2 if Ï‡Ê¹(g)â€„=â€„Î”(g)â€…+â€…1, where Ï‡Ê¹(g) and Î”(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 â‰¥ 1. let fm(g) be a path with m â‰¥ 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 gâ€Ž, â€Ždefined as â€Ždâ€Žq(g)â€„=â€„tr(g)â€…+â€…d(g)â€Ž, â€Žw

##### 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 fÌ‚ : v â†’ {1, 2, â€¦, n} with the property that fÌ‚(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 fâ€„:â€„v(g)â€„â†¦â€„v(g) such that fe(m)â€„=â€„n, where fe(uv)â€„=â

##### 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...

##### 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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