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Ramanujan Graphs Arising as Weighted Galois Covering Graphs

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Formulas for the Computation of the Tutte Polynomial of Graphs with Parallel Classes

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Total Vertex Irregularity Strength of Trees with Maximum Degree Five

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On Classes of Neighborhood Resolving Sets of a Graph

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Formulas for the Computation of the Tutte Polynomial of Graphs with Parallel Classes

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Total Vertex Irregularity Strength of Trees with Maximum Degree Five

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The Eccentric-distance Sum of Some Graphs

Let $G = (V,E)$ be a simple connected graph. Theeccentric-distance sum of $G$ is defined as$\xi^{ds}(G) =\ds\sum_{\{u,v\}\subseteq V(G)} [e(u)+e(v)] d(u,v)$, where $e(u)$ %\dsis the eccentricity of the vertex $u$ in $G$ and $d(u,v)$ is thedistance between $u$ and $v$. In this paper, we establish formulaeto calculate the eccentric-distance sum for some graphs, namelywheel, star, broom, lollipop, double star, friendship, multi-stargraph and the join of $P_{n-2}$ and $P_2$.
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Inverse Graphs Associated with Finite Groups

Let $(\Gamma,*)$ be a finite group and $S$ a possibly empty subset of $\Gamma$ containing its non-self-invertible elements. In this paper, we introduce the inverse graph associated with $\Gamma$ whose set of vertices coincides with $\Gamma$ such that two distinct vertices $u$ and $v$ are adjacent if and only if either $u * v\in S$ or $v * u\in S$. We then investigate its algebraic and combinatorial structures.
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A Note on the Edge Roman Domination in Trees

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Efficient Maximum Matching Algorithms for Trapezoid Graphs

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On the Connectivity of $K$-distance Graphs

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On the Spectrum of a Class of Distance-transitive Graphs

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A Note on the Edge Roman Domination in Trees

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Efficient Maximum Matching Algorithms for Trapezoid Graphs

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Automorphism Group of Certain Power Graphs of Finite Groups

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Note on Parity Factors of Regular Graphs

In this paper, we obtain a sufficient condition for the existence of parity factors in a regular graph in terms of edge-connectivity. Moreover, we also show that our condition is sharp.
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